Names do indeed have to come from the players (note that there's a big
difference between infinite and finite, so even a list of thousands of
names wouldn't be enough). And it's not just star names, everything that
scales up to infinity has to be named by players, including:
The rather silly TBG-1 idea of using ships' names to identify them to the game engine also gets fixed in the general delegation of naming to players, removing the case where startups get rejected for choosing an existing name. Eg "Enterprise (1701)" could meet "Enterprise (666)".
So everything is identified by a unique id number which is revealed to players so things can't be completely hidden by renaming, but the names themselves can be set freely (not just by the first discoverer).
Players only get to rename one thing (in their possession or presence) per turn so there won't be a deluge of renaming everything every turn, but it's possible for players to fight over a name if they really want to. This, and dumb naming in general, is left for other players to police by smacking the guilty.