The U.S.S. Star Hammer is my main toon's ship. Not a really interesting story about that; I used to play a game called Spore and I created a really nifty ship called the Star Hammer (and it's little brother called the Dwarf-Star Hammer. Both ships with a huge spinal mounted cannon) and when I started playing STO I wanted a spiffy sounding ship name so I grabbed that one. :3
My toon Angel Silhouette is a science officer (Unfortunately. I can't stand playing Sci.) and has a few ships with which I alternate:
U.S.S. Omega Point (DSSV: An omega point is the culmination of all knowledge in the universe.)
U.S.S Omniscience (RSSV: A bit like an omega point, really. :p I also like how it can look like omni-science to me sometimes :3)
U.S.S. Star Lion (My Star Cruiser. It looks a bit like a diving frigate bird, to me, but calling it the U.S.S. Frigate would have been silly. So I went from Frigate to Sea Lion, then from Sea Lion to Star Lion. :3 )
U.S.S. Entropy (Nebula Class Starship. I decided to go with the opposite of the culmination of knowledge, one of the generally accepted words for the eventual heat death of the universe.)
My Ferengi has had the U.S.S. Tsar Bomba (The largest nuclear bomb ever detonated on earth) the U.S.S War Machine and now the U.S.S. Tannhauser Gate (Named after a battle in which Roy Batty fought before the events of Blade Runner.)
My borg had:
U.S.S. Bonny Anne (Saber Class Escort Named after one of the most famous woman pirates, Anne Bonny.)
U.S.S. Queen Emeraldas (Akira Class named for the... Queen Emeraldas pirate ship from the anime of the same name. xD)
U.S.S. Scarab (Gallant mish-mash named because it looks like a Scarab Beetle)
I kind of pretend she's a mirror universe Terran Empire captain who practices piracy to both hurt Starfleet and to fund the maintenance on her ships.
Those are the only ones worth mentioning Starfleet side.
My KDF officer had:
The I.K.S. K'argentivas (named after a large, the largest flying bird ever discovered, the argentivas magnificens)
The I.K.S. Blood Bath
The I.K.S. Beast
The appropriately named I.K.S. Can't remember the name just now. Either Behemoth, Juggernaut or Goliath.
and the I.K.S. Warbird (Because it looks very Romulan-esque ^.^ )
Most of the names are just.. sort of klingony sounding except they're in English. :3