Mine's called U.S.S. Aleksey Krupnyk - he is a known personality on StarCraft 2 scene, and I look up to him both for innovative gameplay, as well as very nice attitude and welll, we are also friends, so that's a bonus. And he loves Czech beer too!
My toon James T Cat, flys the USS Kittyprize/NCC-773440
Hes a lolcat version of Kirk and his crew. An RP from an alternate Cat dimension...I use this toon for my FOundry Review videos on youtube :3 look me up sometime, I use the same name all across Google =^.^=
His Shuttle the Meowlileo, is for smaller missions.
Captain: James T Cat
First Officer: Mr Spot
Helm: Mr Mew Wu
Chief Eng: Mongomery the ScottishFold
Chief Med: Dr Leonard McCat
Security Cat: Ensign Generic
I tends to use themes for my ships. Usually the themes arise as I play (so the first ships generally don't follow the theme).
Unfortunately I can't remember all of them, but I can remember these:
For my main Fed, I eventually settled on mythical figures:
USS Nevada (Miranda)
USS Avatar (Heavy cruiser)
USS Prometheus (Akira)
USS Jupiter (Ambassador)
USS Europa (Prometheus)
USS Aurora (Sovereign)
For my new Fed, I decided on celestial objects:
USS Cirrus (Centaur)
USS Southern Cross (Sabre)
USS Andromeda (Cheyenne)
USS Andromeda-A (Galaxy)
Space... The final frontier... These are the voyages of the Federation Starfleet.
Its continuing mission: To explore the same old worlds...
To blow up enemy life and hostile civilizations...
To boldly push F where everyone has done so before!
I named the free bee Voth Carrier the U.S.S. Oriskinay. After the U.S. Carrier that was decommissioned after the Vietnam war. It caught fire, and was gutted, and sunk a few years ago to become a potential coral reef site.
I plan to get the new Klingon ship, I just haven't thought of a name for it yet.