I was rewatching TNG Relics the other day, and something that I always found interesting was that despite Scotty being very well known to audiences, the crew of the Enterprise-D treat him as they would any other guest of the week. It got me wondering -- how well known would Scotty have been to people living in the 24th century, both in and out of Starfleet? How well would any of them have been known? Generals and admirals in real life are known to history buffs, but the general public can only name the most famous, if that. I ran down a list of each major character's best known deeds and I'm curious if people agree. This knowledge is only based on what we see on screen.
TOS
Kirk - Kirk's Enterprise has been shown to have quite the reputation even a century later within Starfleet, however I imagine the general (Federation) public would be largely unaware of his five year mission. I think he would be best known for his stopping the Whale Probe first and foremost, followed by his involvement in the creation of the Genesis planet and barging into the Klingon peace talks at Khitomer.
Spock - Closely associated with Kirk's legacy, I think he would be equally known to later generations as the ambassador to a major galactic power, as well as his (assumed) death during the Romulan supernova.
The rest of the TOS cast - Again, closely associated with Kirk. Sulu might have a slight edge due to being captain during the Praxis incident, but the others would be largely out of public view.
TNG
Picard - By far best known for being assimilated by the Borg and leading the disaster at Wolf 359. Like Kirk, certain missions of the Enterprise-D would be well-known within Starfleet history, and I have to imagine his recounting of the events of The Inner Light and The Chase would have made great splashes in Archaeology circles, but those are smaller groups. It's a bit muddled how much of First Contact would truly have been made public, but it probably would've helped to redeem his image, as well as the events of Picard season 3. Romulan citizens would also probably know him well due to the events of Nemesis, and maybe Klingons for his role in making Gowron chancellor.
Data - Data has been shown to be well-known to other Starfleet officers (Bashir and B'elanna) due to being the first Soong-type android, and I imagine that would extend somewhat to the public. Aside from that, I don't think he would have any deeds that would make him more famous than his Enterprise-D coworkers though.
Worf - Probably fairly well-known in Starfleet for being the first Klingon in the service, as well as his postings on the Enterprise and DS9. However, while Federation citizens might not know him, Klingon ones certainly would. He would have been a footnote on the attack on Khitomer, but famous for slaying Duras and Gowron, as well as being made Klingon ambassador to the Federation under Martok (although that didn't seem to last too long).
Riker - Based only on what we see, Riker would've been well-known for being the captain who stopped the Borg attack following Wolf 359, but would largely play second fiddle to Picard.
The rest of the TNG cast - Maybe Geordi had a great and famous career later on, but solely from what we see on screen, they would've remained largely out of the public eye.
DS9
Sisko - Sisko is a household name on Bajor from the beginning of DS9, and I think he would have been very well-known in Starfleet as the commander of a vital strategic outpost, but that might be it. His most famous actions would probably be the mining of the wormhole and subsequent recapture of DS9, and the signing of the peace treaty on DS9, so military buffs would know him well. Who knows how Federation news reported that business with Dukat right as the war ended.
Odo - As the only Founder on this side of the war, Starfleet brass would've kept a close eye on Odo, and word of his existence would certainly have slipped out as the war raged on. It's possible he was the best known of the DS9 crew, but it's hard to say.
Kira - Probably fairly famous on Bajor due to being the Bajoran liaison to DS9. The Bajoran tabloids would've had a field day with her though.
O'Brien - The most important man who ever lived. Perhaps not the most famous though, he stayed largely out of the limelight.
The rest of the cast - Well-known to history buffs, but I think largely unknown to the average citizen.
Voyager
Voyager as a whole would have been a historical footnote until the midpoint in the series when they re-established contact with the Federation. Following that, they would've been of strategic interest to Starfleet, and possibly fairly well-known publicly, but I think it wasn't until their return to Earth where they became really famous. They're also a rare example of a crew that would've become more well-known as history continued, due to the Federation expanding into the Delta Quadrant and bringing more and more of their adventures to light. Of the crew, Janeway as the captain would've gained the largest recognition, while Seven, as an ex-Borg, probably would've been second (although that certainly didn't help her career). Seven's later involvement with the events of Picard season 3 also would've bolstered her image.
I did struggle to find an event where a single member of the crew would've received more acknowledgement than the others upon their return, with the exception of Threshold. Aside from being trapped in the Delta Quadrant, Janeway and Paris would've been noted as the first to break the Warp 10 barrier, putting them alongside real figures like Chuck Yeager.
Enterprise
Archer - I think of everyone on this list, Archer probably would be the most famous to the public. He and the crew were shown to be pretty publicized at the beginning of the show, but their involvement in the Xindi Crisis would've made them a household name. Even shortly after we're told elementary schools were being renamed after him. His later involvement in the foundation of the Federation means he would've been in every history curriculum going forward.
The others - I don't think any of the others would've gotten the same level as Archer did individually, although they would've also gained attention for the Xindi Crisis. T'Pol broke a number of Vulcan records for staying on a starship, but those would likely have only been known as a curiosity to Vulcan officers. Trip, Phlox, and maybe Hoshi too might have gotten significant notoriety in their fields.
Discovery
Michael Burnam - Probably best known to history as the instigator of the Federation-Klingon War. All of her future actions took place on the classified Discovery, whose existence was completely sealed by Starfleet in the 23rd century. After reappearing in the 31st century however, she would've gained quite a bit of attention in her actions to reunify Starfleet and solve The Burn, easily the best known galactic-wide event of the time. I'll admit to you I haven't seen Seasons 3 onward of Discovery, so I can't give better specifics.
Rest of the crew - Officially forgotten during the 23rd century, they would've been lost to time until their actions during the 31st. Saru as captain would've gained the most infamy during this time.
Lower Decks
Boimer - The namesake of the "Boimler Effect", something never forgotten by future generations.
The rest - They seem rather well-known... by other lower deckers of California-class ships. I guess that's something. Mariner also may have made a name for herself for the events of the end of Lower Decks season 4, but that probably didn't get exposed to the public either.
Strange New Worlds
Pike - He has been shown as the namesake for a number of medals of valor, implying that he has a very positive reputation around Starfleet, even during his life. However, I don't think he would be very well-known. The best evidence of that is that his best known event to audiences, that of his eventual fate, is completely classified in-universe.
Rest of the crew - Number One might be of legal significance in the future, but that's about it. I do get the impression the show is building up to something big for La'an, but we'll have to wait and see.
Prodigy
I've never seen Prodigy, however from what I know of it they are completely obscure characters to the larger galaxy.
TOS
Kirk - Kirk's Enterprise has been shown to have quite the reputation even a century later within Starfleet, however I imagine the general (Federation) public would be largely unaware of his five year mission. I think he would be best known for his stopping the Whale Probe first and foremost, followed by his involvement in the creation of the Genesis planet and barging into the Klingon peace talks at Khitomer.
Spock - Closely associated with Kirk's legacy, I think he would be equally known to later generations as the ambassador to a major galactic power, as well as his (assumed) death during the Romulan supernova.
The rest of the TOS cast - Again, closely associated with Kirk. Sulu might have a slight edge due to being captain during the Praxis incident, but the others would be largely out of public view.
TNG
Picard - By far best known for being assimilated by the Borg and leading the disaster at Wolf 359. Like Kirk, certain missions of the Enterprise-D would be well-known within Starfleet history, and I have to imagine his recounting of the events of The Inner Light and The Chase would have made great splashes in Archaeology circles, but those are smaller groups. It's a bit muddled how much of First Contact would truly have been made public, but it probably would've helped to redeem his image, as well as the events of Picard season 3. Romulan citizens would also probably know him well due to the events of Nemesis, and maybe Klingons for his role in making Gowron chancellor.
Data - Data has been shown to be well-known to other Starfleet officers (Bashir and B'elanna) due to being the first Soong-type android, and I imagine that would extend somewhat to the public. Aside from that, I don't think he would have any deeds that would make him more famous than his Enterprise-D coworkers though.
Worf - Probably fairly well-known in Starfleet for being the first Klingon in the service, as well as his postings on the Enterprise and DS9. However, while Federation citizens might not know him, Klingon ones certainly would. He would have been a footnote on the attack on Khitomer, but famous for slaying Duras and Gowron, as well as being made Klingon ambassador to the Federation under Martok (although that didn't seem to last too long).
Riker - Based only on what we see, Riker would've been well-known for being the captain who stopped the Borg attack following Wolf 359, but would largely play second fiddle to Picard.
The rest of the TNG cast - Maybe Geordi had a great and famous career later on, but solely from what we see on screen, they would've remained largely out of the public eye.
DS9
Sisko - Sisko is a household name on Bajor from the beginning of DS9, and I think he would have been very well-known in Starfleet as the commander of a vital strategic outpost, but that might be it. His most famous actions would probably be the mining of the wormhole and subsequent recapture of DS9, and the signing of the peace treaty on DS9, so military buffs would know him well. Who knows how Federation news reported that business with Dukat right as the war ended.
Odo - As the only Founder on this side of the war, Starfleet brass would've kept a close eye on Odo, and word of his existence would certainly have slipped out as the war raged on. It's possible he was the best known of the DS9 crew, but it's hard to say.
Kira - Probably fairly famous on Bajor due to being the Bajoran liaison to DS9. The Bajoran tabloids would've had a field day with her though.
O'Brien - The most important man who ever lived. Perhaps not the most famous though, he stayed largely out of the limelight.
The rest of the cast - Well-known to history buffs, but I think largely unknown to the average citizen.
Voyager
Voyager as a whole would have been a historical footnote until the midpoint in the series when they re-established contact with the Federation. Following that, they would've been of strategic interest to Starfleet, and possibly fairly well-known publicly, but I think it wasn't until their return to Earth where they became really famous. They're also a rare example of a crew that would've become more well-known as history continued, due to the Federation expanding into the Delta Quadrant and bringing more and more of their adventures to light. Of the crew, Janeway as the captain would've gained the largest recognition, while Seven, as an ex-Borg, probably would've been second (although that certainly didn't help her career). Seven's later involvement with the events of Picard season 3 also would've bolstered her image.
I did struggle to find an event where a single member of the crew would've received more acknowledgement than the others upon their return, with the exception of Threshold. Aside from being trapped in the Delta Quadrant, Janeway and Paris would've been noted as the first to break the Warp 10 barrier, putting them alongside real figures like Chuck Yeager.
Enterprise
Archer - I think of everyone on this list, Archer probably would be the most famous to the public. He and the crew were shown to be pretty publicized at the beginning of the show, but their involvement in the Xindi Crisis would've made them a household name. Even shortly after we're told elementary schools were being renamed after him. His later involvement in the foundation of the Federation means he would've been in every history curriculum going forward.
The others - I don't think any of the others would've gotten the same level as Archer did individually, although they would've also gained attention for the Xindi Crisis. T'Pol broke a number of Vulcan records for staying on a starship, but those would likely have only been known as a curiosity to Vulcan officers. Trip, Phlox, and maybe Hoshi too might have gotten significant notoriety in their fields.
Discovery
Michael Burnam - Probably best known to history as the instigator of the Federation-Klingon War. All of her future actions took place on the classified Discovery, whose existence was completely sealed by Starfleet in the 23rd century. After reappearing in the 31st century however, she would've gained quite a bit of attention in her actions to reunify Starfleet and solve The Burn, easily the best known galactic-wide event of the time. I'll admit to you I haven't seen Seasons 3 onward of Discovery, so I can't give better specifics.
Rest of the crew - Officially forgotten during the 23rd century, they would've been lost to time until their actions during the 31st. Saru as captain would've gained the most infamy during this time.
Lower Decks
Boimer - The namesake of the "Boimler Effect", something never forgotten by future generations.
The rest - They seem rather well-known... by other lower deckers of California-class ships. I guess that's something. Mariner also may have made a name for herself for the events of the end of Lower Decks season 4, but that probably didn't get exposed to the public either.
Strange New Worlds
Pike - He has been shown as the namesake for a number of medals of valor, implying that he has a very positive reputation around Starfleet, even during his life. However, I don't think he would be very well-known. The best evidence of that is that his best known event to audiences, that of his eventual fate, is completely classified in-universe.
Rest of the crew - Number One might be of legal significance in the future, but that's about it. I do get the impression the show is building up to something big for La'an, but we'll have to wait and see.
Prodigy
I've never seen Prodigy, however from what I know of it they are completely obscure characters to the larger galaxy.