I think the implication was that all these figures were dead before the commissioning, but FASA didn't want to make such a statement of Kirk or Spock (although Sulu, Scotty, and Uhura are fine, I guess).
That's an interesting question. Does Starfleet name ships after living people? In USN precedent, this is now prominently true: Carl Vinson was alive to see the launch of "his" carrier, and George Bush the elder didn't even cut it close with "his".
Of course, in RN, Queen Elizabeth is still going strong after the launch of "her" respective carrier, even though it can be argued (and is) that the ship, like her immediate name-predecessor, was named in honor of Elizabeth I rather than II. Everything can be made vague like that, even if it isn't intended to be: perhaps a putative
USS Picard in 2378 honors that other naval figure from the Trafalgar days, perhaps
USS Kirk in 2278 is named after George, etc.
Conversely, though, we would have to invent Trek people in order to establish they were alive when ships were named after them. We know Surak and Gorkon were dead long before starships with registries in the five digits would have been a thing; indeed, them being dead is what made them eligible for Starfleet fame in the first place. But an officer from the Archer family (well, not necessarily the "same" family) was alive in the 2250s of the Kelvin timeline - is a living Archer the namesake of the vessel named in ST:NEM? Nothing to tell either way. So we only lack solid proof of living namesakes; we don't have solid proof
against such, even through absence.
Timo Saloniemi