USS Bevan (named after Aneurin 'Nye' Bevan) would be a good name for a hospital starship, whether Olympic class or otherwise.
The USS Lacking In Gravitas, one of the Parody-class starships Serious answer, USS Malevolence, great ship name that popped up from time to time on Star Trek: Armada
I'd name mine the Copernicus, to honor the first person who realized Earth and humanity weren't at the center of the universe.
uss phoenix natually. lol it would be of romulan design. prototype self repairing ship, i.e. can whitstand devastating damage and still be able to reform itself... to an extent... even without a crew.
Roguephoenix, what happened to the Nebula class Phoenix, if it's no longer in service your Phoenix could replace it? Self repairing sounds like Borg tech! James
There was a U.S.S. Soyuz, but probably not the U.S.S. Sovyetsky Soyuz, although presumably that'd be at least as appropriate as the U.S.S. Yamato. I'd like to see a U.S.S. Vostok, Gagarin, and maybe a Mir. Obviously, I also like U.S.S. Revenge, named after the Revenge-class Royal Navy battleship that fought at Jutland and the Resolution-class Royal Navy SSBN in service until 1994 or 1995.
I don't see why not. IJN ships are represented, so why not the DKM? I've always been partial to the name Graf Zeppelin myself.