For my primary character, I named my ships after carriers, battleships,battlecruisers, or heavy cruisers of the world's navies at around WW2. The only exception is my NX class ship which is named after a space shuttle.
Sovereign- USS Bismarck
Galaxy X- USS Midway
Luna- USS Tennessee
Excelsior refit- USS Hood (which is also a canon ship)
Prometheus- USS North Carolina
Intrepid refit- USS Guam
TOS Constitution- USS Iowa
NX- USS Discovery
I have a captain's yacht also, but it still has the random name from the game. I haven't quite figured out what to name it yet.
My other character's ships:
NX- USS Atlantis
Miranda- USS Valley Forge
Constitution refit- USS Lexington
Nova- USS Mercury
Captain's Yacht- USS Gallileo
USS Warsong-first thing I came up with in beta kinda stuck with me, it's from WoW warsong gulch pvp area
USS Legacy- each ship that I kept "canon" a kind of honor to it/ them
USS Deviant- I modeled my science toon from my avatar which I recently discovered is from deviantart.com
Galaxy X - USS Imperator. Shortened from Imperator Maximus, Latin for Great Commander.
Prometheus - USS Cerberus. Named after the Greek three headed dog.
Nebula - USS Redemption. Named after the medical frigate in Star Wars.
Intrepid - USS Salvation. Named after the sister ship of the Redemption. (Could be off on that one)
Defiant - USS Rebuke. Named for the definition of the word.
Sovereign - USS Resolute. I liked the name.
Peregrine - USS Seraph . Names as a reference to the DS9 episode, "Sacrifice of Angels"
Delta Flyer - USS Twilight Mirage. Named after a ship I'll some say write about.
Class F Shuttle - USS Classic. It's a classic.
Science Vessel - USS Aurora. Named after an Aurora Borealis.
Light Cruiser - USS Cavalier. First thing that came to mind at the time.
Naming my ships is always an agonizing process. I do like to have specific reasons or themes for my ship names.
Here are a few I can recall off the top of my head.
USS Daedalus (Prometheus class MVAM) - Stuck with the Greek-theme to match the ship class name, and its a Stargate SG1 reference
USS Fearless (refit Excelsior) - Named for the USS Fearless (NCC-14598). I even tried to keep the registry more or less intact. She is intended to be the refit of the same ship. (STILL in service )
USS Baltimore (Star Cruiser) - Named for the city where I live.
USS Majestic (Galaxy Class) - Named for the USS Majestic (NCC-31060). I kept the registry and added a -A. She is intended to be a Galaxy that was under construction during the Dominion War that was named for the ship that was destroyed in Operation Return. Still in service in 2409.
Here are some names I came up with for the ships my current roster of characters use/have used:
USS Sullivans: named after the modern Arliegh Burke-class destroyer. She was the first ship of my Tactical character on his first run.
USS Hamilton: the first ship of my Tac on his second run. Named after my family name.
USS Kumari - Ushaan-class; named after Shran's ship in ENT
USS Grimlock - Akira-class, named after a Transformers character
USS Zea Dorsa - Vigilant-class, named after a plain on Mars
USS Kearsarge - Cerberus-class, named after the US warship that sank the Confederate raider Alabama.
USS Keokuk - named after a Union experimental ironclad from the Civil War. In my Eng's first run, the name was actually used for her second ship, a Constitution-class. For her reset, I felt it was more appropriate for a Centaur-class
USS Sumter - named after one of the first Confederate raiders. It was a Centaur-class ship during the character's original build-up, but seemed more fitting for a Constitution-class starship this run.
USS Albemarle - named after a Confederate river ironclad (seeing a theme here? ). Used for both a Dakota and Sovereign class starship.
USS Shenandoah - a Galaxy-class starship named after another Confederate raider, the only one to circumnavigate the globe.
USS Housatonic - planned name for an Excelsior-class starship. Named after the Union warship sunk by the Confederate submarine H.L. Hunley.
USS H.L. Hunley - Delta Flyer, named after - well, see above. I though the historical irony was delicious.
USS Terra Nova - named after one of the first expeditions to explore the Antarctic. On my first Fed Sci, the ship was a Miranda-class; on my current character, it was an NX-class. The NX was replaced by an Oberth since then.
USS Sojourner - Nova-class ship, named after the Mars rover.
USS Resolution - a Hope-class ship, named after Captain James Cook's favorite ship. This ship by my first Sci until the Nebula was released.
USS Cassini - Nebula-class starship, named after one of the probes that explored Saturn. This was the final ship of my first Sci character before she was deleted, and the third ship for my current Sci.
USS Atlantis - Discovery-class ship, named after the Space Shuttle of the same name. The last ship of my current sci before...
USS Godspeed - Trident-class starship, named after one of the three ships that carried the English colonists to what would become Jamestown. Was originally the name of my first Sci character's Nova-class starship, but I grew fond of the name and decided for my new sci, I'd save it for the "end" ship. I did, however, give in the registration "NCC-140507-A" in honor of that first ship.
IKS Ravage - Bird of Prey, named after the Transformers character. I was at a loss for a better name.
IKS Wy'vex - K'Tanco-class battlecruiser; named after the wyvern dragons of mytholgy.
IKS Ra'kyri - K't'inga-class battlecruiser; named after a fictional race I keep trying to write about.
IKS Lohikaarme - Negh'Var-class battlecruiser; named after a dragon from what I believe is Scandinavian mythology.
IKS Drahkos - a sort of play on the word "dragon;" which I thought was fitting for a Gorn. Used for both a Vor'cha attack cruiser and Varanus FSV.
All the ships for my Klingon Science character are named after gods of war. I'm not sure of the origins of all of them, so I suggest you look them up if you're curious:
IKS Guan Yu