My current ships for my alt are named after famous capitals of ancient Empires
For my main my ships are differently named.
The USS Caesar
The USS Funk (Olympic class )
The USS Phantasmagoria (A running joke with a friend who likes the Spoony ones videos)
The USS Qwib Qwib (A proud ship!)
The USS Valdez (Named after the oil tanker in Fallout 2)
USS Sagan - Named after the great science popularizer Carl Sagan who did more for bringing science into the home than just about anyone else in the latter half of the 20th century. A visionary, a skeptic and a true humanist. We were robbed of a great man way, way to early. As a people we would be so much better for having him with us.
USS Arroway - Named after Eleanor Arroway in the novel 'Contact' by Carl Sagan. A wonderful character who's wonder of the universe is a projection of Carl's own admiration and fascination with all things of the Cosmos.
USS Skeptic - A scientific skeptic is one who questions the reliability of certain kinds of claims by subjecting them to a systematic investigation. For a DSSV I considered the name very apt.
USS Nautilus (Prometheus - Class) The submarine from the Jules Verne novels "Twenty Thousand Leagues under the Sea" and "The Mysterious Island." Also, I found a totally sweet desktop wallpaper of a Federation Starship 8 or so years ago called the Nautilus and have loved the name ever since.
USS Masamune (Maelstrom/Gryphon kitbash) Japan's greatest swordsmith.
USS Muramasa (Defiant/Vigilant kitbash) Another Japanese swordsmith, whose own madness and violent tendencies were said to have been passed to the blades he made, and as such are thought of as cursed blades that create a bloodlust in those who wield them.
USS Excalibur (Noble/Sovereign kitbash) King Arthur's fabled Sword. However, my main reason for naming it this is as an homage to the Ambassador - class and later Galaxy - class USS Excalibur from the Star Trek: New Frontier book series.
USS Eureka (Luna - Class) Named for the Syfy series Eureka. Seemed fitting.
Shinano and Campbeltown were both named after WWII warships. Shinano was sister ship of the Yamato and Musashi, both of which also had Galaxy class ships named after them. HMS Campbeltown was packed full of explosives and rammed into a German drydock, which is a really awesome story you should read more about.
I've had other ships, of course, but when I can't think of an appropriate name, I just reach into the grab bag of mythology and pull out a god or goddess. It feels lame and unoriginal, but they're still good names for starships.
Named for schoolteacher Christa McAuliffe, who died in the Challenger space shuttle explosion. The ship's registry marks the date (minus the required 9 prefix): 1986. Did you know that according to official nomenclature, the late Mrs. McAuliffe doesn't actually qualify as an astronaut? Has to do with altitude reached. Fortunately, they gave it to her anyway.
Patton (Miranda-Shi Kar-Centuar mix) : Named after General George S. Patton, US General during World War II, died of injuries sustained from car crash in 1945.
Rommel (that's my Constitution): Named after Field Marshal Erwin Rommel, German leader during World War II, died of self-poisining to save family from retrubution after being mistakenly assosiated (although sympahtised) with Operation Valkerye, the plot to kill Hitler in 1944.
I plan to name all of my ships after World War II leaders, including C aptain Winters of Easy Company, 506th PIR, 101st Airborne. Watch Band of Brothers if you don't know him.