You are conflating 2 different things. the Ship's name is the USS Enterprise. No Letter at the end. the Ship's Nickname is the Enterprise D. Not as catchy as "The Big E" but just as unofficial.
They should hire The Donald when his term runs out in January. He's really good at destroying things! Isn't it possible that when DIscovery hit that "bump in the road" on the way to the 32nd Century, she may have been duplicated by some weird temporal shenanigans just like Riker in "Second Chances" (TNG) It would explain pretty much all of the difference between "Calypso" and where we are now. Either that Zora is off on her own choosing to hide from everybody, or She's in a different timeline.
Who knows how Calypso fits into the story. Maybe there will be an episode where the Discovery-A comes across the original Discovery and they're just as confused as to why so they leave it somewhere no-one can find.
Yes, it did! Though I'm afraid the serialized format doesn't allow whole episodes dedicated to a holodeck romp.
I'm so glad someone said this before me! Not only does programmable matter make it possible for the Discovery to look like it wants, I think it plays into other themes of transformation/transition that are being developed this season: being allowed to present oneself as one wants.
In regards to Disco's registry letter addon... According to official records, the USS Discovery was destroyed in 2258. Given the Temporal Accords and sensitive nature of how Disco found itself in the 32nd century (time travel - despite the fact it was done to preserve all sentient life in the universe), on a larger scale, I would imagine that the addition of letter 'A' to its registry during the refit was done to make it look like Disco is a different ship (a successor of the original if you will) as far as the general public is concerned. It seems that with the latest episode, we know that apart from some Starfleet officers and certain individuals on Vulcan, no one else really knows about Discovery's real background (sans the 1 surviving colonist from 'The colony' and that thug - what's his name). For all we know, Starfleet may have made up a credible story about Disco to brief other SF captains - and apart from the ships at HQ, no one else in Starfleet saw Disco in its original form (apart from Earth, but its no longer part of the Federation and they have no idea about Disco's time travel). Calypso could still tie into canon. As someone mentioned before, because of programmable matter, Zora could have decided to return Discovery to its original 23rd century look while waiting (although, why she would decide to do so is a bit... strange... unless another Time Travel episode occurred and in order to get back to the 32nd century, Disco needed to wait in a nebula - likely in its original form so as to not arouse suspicion - or it may have been stripped of its 32nd century tech and returned to 23rd century standard and left to evolve on its own). We still don't know whether Calypso will be tied into the rest of S3... and to be fair, I sort of see Calypso as a 'drawing board' for Season 3. A good standalone story that doesn't specifically have to be explained within the larger canon (although you technically could)