I usually hate the names the ships first come with, so I always change them. I change the names of buildings as I please. But some buildings, like inns, I have a name that I use over and over in every game. I usually have only one inn on the island, so I need not worry about coming up with a different name for multiple inns.
Inn - The Dead Parrot Inn (from Quest for Glory V)
Now onto ship names:
Snow - Scout
Schooner - Faithful Scout or Swift Wind
Sloop - Battle Dog
Brig - Scout (I know, I use that name for Snows. But I so rarely build these underarmed ships that I don't really care what their name is, that is, unless the original name really stinks. If I do build this class of ship, I use it for raids and long-range scouting missions.)
Frigate - Freedom's Light, Outlaw Star (from the anime show "Outlaw Star"
), Battle Flag, or Pirate Moon.
Galleon - Geomancer, Rememberance (if I had a beloved ship sunk), or Arch Angel.