FPS Rhyddid. It's Welsh for "freedom", and FPS is short for Free Peoples Ship, a reflection of the alternate universe Avalias comes from.

My Ship is Called U.S.S. BULLDOG Nebula Class.
HMS Bulldog was a B-class destroyer of the British Royal Navy that saw service throughout World War II, seeing service on convoy duty in the Atlantic and Arctic. Her most notable action was the first naval capture of a complete Enigma machine and coding documents from the German submarine U-110 on 9 May 1941.
As an Ex Royal Navy Man I couldn't resist

USS Kitana
from Mortal Kombat, Princess of Edenia, was somehow fitting for my Intrepid

USS Charon
Luna Class... so I simply took another Sol-System Moon

USS Charybdis
Oddy... this should be as obvious as the one above

My retro defiant class is called U.S.S. Viper, after the colonial fighter crafts in Battlestar Galactica. It has the serial number of Starbuck's dogtags (from the new series) with an X on the end. Because I feel a Defiant class needs an X on it somewhere.

The new USS Merrimac..... The Merrimac was one of the first ironclad ships, so a Defiant class is probably one of the first of its kind...

All my ship names are drawn from British ships that fought at Trafalgar:

• U.S.S. Bellerophon: (Click to view Wikipedia article)
  Known to sailors as the "Billy Ruffian", she fought in three fleet actions, the Glorious First of June, the Battle of the Nile and the Battle of Trafalgar, and was the ship Napoleon finally surrendered aboard.
  Named after the Greek warrior who rode the winged horse Pegasus and slew the monster Chimera.

• U.S.S. Euryalus:
  A 36-gun frigate which took on survivors from the French ships, as well as the captured French Admiral Pierre de Villeneuve.
  In the Odyssey, Euryalus is a Phaeacian youth. Homer gives him the epithet "the peer of murderous Ares".

• U.S.S. Leviathan:
  Under Henry William Bayntun, she was near the front of the windward column led by Nelson, and captured the Spanish ship San Augustin.
  Leviathan is a sea monster referred to in the Bible. In Demonology, the Leviathan is one of the seven princes of Hell and its gatekeeper.

• U.S.S. Polyphemus:
  Fighting in the lee column; she engaged the French ships Neptune and Achille and after the battle towed HMS Victory, carrying Nelson's body, back to Gibraltar.
  A gigantic one-eyed son of Poseidon and Thoosa in Greek mythology, one of the Cyclopes. His name means "much spoken of" or "famous". Polyphemus plays a pivotal role in Homer's Odyssey.

• U.S.S. Temeraire:
  During the battle "The Fighting Temeraire" came to the rescue of the beleaguered Victory, and simultaneously fought and captured two French ships, winning public renown in Britain.
  Her final voyage was depicted in a J. M. W. Turner oil painting of critical acclaim, entitled The Fighting Temeraire tugged to her last Berth to be broken up, 1838.

My best friend gave me a D'Kora. So while I have no luck at gambling, I apparently am pretty lucky!

I named my new shiny ship The USS Bernie Madoff. Now I just need to figure out a good STO ponzi scheme for billions! Muahahahaha!

Oh... My Frerengi Captain is Damon Wayans.

Mine is the U.S.S. Asclepius, named after the god of healing in Greek mythology.

And to give the short version of why I came into that name, is that due to unfortunate events, the previous captain of the starship -who was also a well skilled doctor-, was discharged of his duties, and the new captain decided to rename the ship to Asclepius in tribute to the previous captain.

(And I know there isn't a moon named Asclepius in the sol system, but I'm going to pretend that one moon was discovered and it was named Ascleipus. )

U.S.S. Republic. Named for the ship Kirk served on as a Lt.

USS Missouri - Live in Missouri and well the Missouri in the US navy is quite famous so picked for that reason.

USS Vir Domus - Simple Translation is Hero's Home.. We live on our ships and we are the Hero's of our story so thought it was pretty good name but thought the Latin version sounded cooler.

USS O'Niell - Stargate SG1 fan...