I can't tell if you're trolling or bored.
Why else did they decide to go with Starfleet after already calling the organization the United Earth Space Probe Agency?
Because it sounds marble-mouthed and "You Spa" sounds like a feminine-hygiene brand.
Very few Star Trek episodes have been featured underwater aliens, and the Federation Naval Patrol was established in one of the last ones it could have been featured in, and even that wasn't possible given it was a Voyager episode and you have the whole nagging problem of them being stranded in the Delta Quadrant.
If it were more intriguing, VOY had two seasons still to do something with it. And ENT is the 24th C. in the 22nd -- they'd have brought over some version of it. There's also the books and games.
Isn't that more or less Vash?
"Captains Holiday" was a great episode, but they made her Maid Marian instead of
Marian Ravenwood in her next appearance. She and Crusher should have been sword-fighting like the boys in that episode, but were relegated to being damsels and dropping clay pots on enemy soldiers' heads.
In the original show they said "the star fleet" the same way a Navy man might say "the fleet." and it must have just caught at some point to become the actual name of the organisation.
They tried a few different ideas before going with Starfleet. I think Ex Astris Scientia or someplace did an article on different possibilities...wasn't one Space Central, or something? Once they went with the short but descriptive Starfleet, or rather, and especially after decades of its success, that should have been the precedent-setter.
EDIT: A good episode(s) to have featured the Federation archeological body could have been "Gambit." Imagine Indiana Picard off on another adventure a la "Captain's Holiday" for the Archeological Council or something, leading to his eventual rescue by the Enterprise. "The Chase" could have included them as baddies trying to thwart Prof. Galen maybe?
Or it could have shown up on DS9 as discoveries were being made in the GQ. Later on in the Dominion Iconian episode too. On VOY, maybe one of the Maquis was previously AC or one of the Starfleeters? Maybe Season 6 included a Paris holonovel with him in the Naval Patrol that turns into
20,000 Leagues Under the Sea...though they kind of did that Season 4 with "Year of Hell."