Adm. Sills, my main alter ego, started on the Science track, so his ships have been named after famous scientists - the Turing, the Mendeleev, the Babbage, and so forth. His current ship is an Odyssey-class, the USS Hans Asperger.
Capt. Sajak came up through Tactical, so his ships are named after military SF authors - the Haldeman, the David Drake, and such. Currently, he's flying the Defiant-class USS John Ringo. (His final ship will be named the USS Pournelle.) His one variation from this was his Ambassador-class ship, the Sarek.
Capt. T'Song's ship reflect her Vulcan heritage - the Vulcan's Forge, the T'Planahath, and the S'harien (it seemed appropriate that a warship commanded by a Vulcan be named for Vulcan's most famous pre-Sundering swordsmith). Her current ship is the long-range science vessel USS T'Pau.
Visigoth, A-F so far. She's been everything from a Defiant to a (I think) Miranda to a mirror escort and beyond. I was going to name my Atrox the 'Obelisk', but I went for the Kumari escort instead so the Visigoth handle lives on.
90% because 'visigoth' sounds cool.
But also it's a reference to asymmetrical warfare and winning against the odds, the Visigoths being a people that helped take down the Roman empire. The Visigoth's captain is an SI operative who finds Starfleet ethical guidelines most often just get in the way. She likes to think of herself as the underdog, alone behind enemy lines, doing what it takes to get it done.
I have a Fleet Patrol Escort named the USS Valkyrie (I figured a fitting name, I wanted something warrior-like).
I have a Fleet Assault Cruiser named the USS Sentinel (for the reason that Sentinels are suppose to be strong and supporting, and I wanted something to reflect that).
I have a Support Cruiser (Ambassador) named the USS Red October (I've always liked this name for some odd reason; first heard it on a film (something to do with a submarine) and for some reason or other, I've always applied it to Ambassador Class Starships).
I also have a Cardassian Galor Class Cruiser named the USS Ghemor (in honour of Tekeny Ghemor from DS9).
I have a Breen Chel Grett Class Cruiser named the USS Ushaan (because I have an Andorian Captain and figured it a good name in recognition of the Andorian tradition.
I have a Jem'Hadar Escort Carrier that I've named the USS Taran'atar (after the first Jem Hadar sent by Odo to learn the way of the Solids).
These are all on my main FED toon. I also have a secondary FED toon and a single KDF toon, though I can't for the life of me remember the shipnames for those two.
In Arthurian legend, Leodegrance is the father of Queen Guinevere and entrusted with keeping the Round table following the death of Uther Pendragon, King Arthur's father. Agravain, brother to the knights Gawain and Gareth, is often something of a not-always unsympathetic heel, and in later tellings usually plays a pivotal role, along with Mordred, in the exposure of Lancelot and Guinevere's affair.
The pair of Birds of Prey, G?e Derg (the larger, red spear) and G?e Buide (the shorter, yellow spear) are named after the twin spears wielded by Diarmuid Ua Duibhne, a character hailing from the Fenian cycle of Irish mythology, and were famed for delivering a wound none could recover from. The Qin, G?e Bolg (traditionally translated as "Belly Spear") was a spear wielded by the hero C? Chulainn who appears in the Ulster cycle of Irish mythology and famed for needing to be cut out of a person as, once stabbed by it, it would send barbs out through the victim's body piercing every one of its joints. L?in Celtchair is a famous fiery lance or spear belonging to Celtchar mac Uthechar and appearing in the Ulster cycle. It is also quite famous for having such great bloodlust that it must be dipped in a cauldron of poisoned blood to be controlled or it would kill the wielder of it.
If you support Science Bridge Officer powers not being affected by Tactical Captain powers then you need to stop drinking the Kool-Aid.
If you think Tactical Captains in Escorts rule PvP you should call your local Poison Control Center immediately.
Captain One-Who-Questions (alien), Science: U.S.S. Dian Fossey, providing your Gravity Well needs in style. All vessels have been named after notable female scientists.
Shuttle name: Oh'Shora (homeworld of her species)
Captain Defends-Like-Stone (same alien species as above), Tactical: U.S.S. Hyppolyta. I shoot, things tend to die. It seems to work. All ships have been named after famous historical amazons.
Shuttle name: Gladius
Captain Cassandra Baker, Trill Engineer: U.S.S. King's Row (a nod to my late home of City of Heroes). I'm sorry, were you trying to punch through my shields and hull? I didn't notice. Up until the current ship, all ships have been named after famous sieges (Massada, Stalingrad, Gibralter, etc).
Shuttle name: Cramped. (in character she HATES shuttles and runabouts.)
Captain Lodwynne, Orion Pirate (who occasionally does side work for the Empire. "Yeah yeah, Qapla'. Now where's my latinum?"): Garumba Siege Destroyer; IKS Red Feather. Previous theme was very Ferengi. Naked Profit, Green Envy. Sadly 'Stand and Deliver' wouldn't fit.
Shuttle name: IKS Small Change.
Most of my ships are named after US aircraft carriers...even though I'm not American, I like their names. Their registry numbers are also inspired by the CV registries of their namesakes.
USS Langley - NX-91010 - Odyssey Class Prototype
USS Lexington - NCC-91002 - Armitage Class Heavy Escort Carrier
USS Saratoga - NCC-91003-F - Odyssey Class Science Cruiser
USS Ranger - NCC-91004 - Chimera Class Heavy Destroyer
USS Yorktown - NCC-91005-C - Ambassador Class Support Cruiser Retrofit
USS Enterprize - NCC-91006-D - Galaxy Class Exploration Cruiser Retrofit
USS Wasp - NCC-91007-B - Excelsior Class Heavy Cruiser Retrofit
USS Hornet - NCC-91008 - Steamrunner Class Blockade Runner Retrofit
USS Essex - NCC-91009 - Defiant Class Tactical Escort Retrofit
USS Intrepid - NCC-91011-E - Sovereign Class Assault Cruiser
And the ones not named after carriers...
USS Regina - NX-91334 - Fleet Aquarius Destroyer
USS Eddard Stark - NCC-91100 - Breen Chel Grett Warship
IGS Rose Tyler - AT-91012 - Andorian Charal Escort
I have two ships in mind for Captain Denny Kidd, the gentleman pirate of Starfleet:
His current and future fleet ride is the Dervish-class escort U.S.S. Emden, NCC-96415. Named in honor of the last gentleman pirate ship of the 20th century, the S.M.S. Emden. I always felt Starfleet needed more German ships, this was one that didn't have negative historical connotations.
His other future ride will be the Sovereign-class cruiser refit U.S.S. Black Prince. Named less after Prince Edward, more after the ships of the Royal Navy to carry the name, and mostly because its a badass name to put on your flagship cruiser.
I actually hold two accounts on STO ~ the second to provide a playing partner for guests (family and friends) and also to help with Foundry Projects.
Y4ArtU ~ aka Jason 'Nemesis' Journey (don't ask! The legacy of those names is complicated :-) flies a variety of ships all named after specific medical illnesses, conditions, or causes of my significant disabilities and this is a way of laughing at my condition, so...
Atrox Carrier ~ USS Neuroborreliosis ~ Tertiary Lyme Disease
Stealth Fighter ~ USS Borrelia ~ The Bacterial Spirochete responsible
Shuttle ~ USS Spirochete ~ The generic for Borrelia
Other ships include:- USS Lymphocytosis, USS Tetra-Paresis, USS Paresthesia, USS Ataxia, USS Hylar-Infarct, USS Polycythemia, and USS Triple-Infection (a Multi-Vector Advanced Escort = Three hulls).
New ships tend to be named after their class until I think of a suitable name and also names get reallocated around the ships once in a while but; all ships are numbered NX-96669-(X) which reflects exactly how often the number 666 has featured in my life :-)
Hence, my most recent acquisition, an Andorian Kumari Escort triple pack is temporarily named USS Kumari T5E4S2 to remind me how many slots it has ~ As an aside, the weapon layout for this escort makes for interesting configurations and tactics. I have developed two methods depending upon the situation ~ first Blast through doing as much damage as possible and out the other side to repair and then repeat, or; Stand-off at extreme range and maintain a maximum power and rate of fire barrage to overwhelm the defences. This is tailored by the weapons and slots configuration. Incidentally, I carry the 3 Kumari universal units in the Tactical tray slots.
My second 'Guest' account ~ Jason 'Nemesis' Aeson's ships are very boring and named USS Argo-A, or B, or C, or D, &c... ~ In Greek Argonaut mythology, Aeson was Jason's father.