I do a little research when I name a ship, just because...
U.S.S. Paramore - A Band I like.
U.S.S. Andor - My char is Andorian, its her homeworld.
U.S.S. Annapolis - My home town and the actual USS Annapolis (SSN-760), is the tenth "improved" Los Angeles-class submarine. USS Annapolis is the fourth ship of the United States Navy to be named for Annapolis, Maryland, site of the United States Naval Academy. So I thought it was kind like "There has always been a ship named Enterprise".
* USS Annapolis (PG-10), a gunboat commissioned in 1897 and in periodic service until 1919, then used as a training ship until 1940
* USS Annapolis (PF-15), a Tacoma-class patrol frigate in service from 1944 to 1946, and sold to Mexico in 1947
* USS Annapolis (AGMR-1), the USS Gilbert Islands (CVE-107) escort carrier renamed Annapolis (AGMR-1) in 1963
* USS Annapolis (SSN-760), a Los Angeles-class submarine commissioned in 1992
* USS Annapolis (NCC-93539) Cheyenne Class Heavy Cruiser assigned to Exploration Foundation Fleet Command.
U.S.S. Chesapeake - Chesapeake Bay in my home state, the original U.S.S. Chesapeake was under the command of Captain James Lawrence and was defeated by the HMS Shannon in 1813. (War of 1812) I took Capt. Lawrence's dying order to his First Officer as my ship's motto; "Don't give up the ship", kind of fitting.
* USS Chesapeake (1799), a 38-gun frigate in commission from 1800 to 1813
* USS Chesapeake, a sloop which was renamed USS Patapsco (1799) in 1799 while still under construction, launched in 1799, and sold in 1801
* USS Chesapeake, a bark which served as a training ship from 1900 to 1910, was renamed USS Severn (1898) in 1905, and served as a submarine tender from 1910 until decommissioned in 1916
* USS Chesapeake (ID-3395), a salvage ship in commission from March to October 1919
* SS Chesapeake (AOT-5084), a transport tanker placed in non-commissioned Military Sealift Command service in 2000
*USS Chesapeake (NCC-93369) Defiant Class Tactical Escort assigned to Exploration Foundation Fleet Command.
U.S.S. Potomac - Potomac River near Washington DC, sight of the Battle of the Potomac during the Civil War. The actual USS Potomac served as Franklin Delano Roosevelt’s Presidential Yacht until his death in 1945.
* USS Potomac (1822), a frigate in commission from 1831 to 1877
* USS Potomac (1861), a whaler purchased in 1861 and sunk as part of the "Stone Fleet" in 1862
* USS Potomac (AT-50), a tug in commission from 1898 to 1922
* USS Potomac (AG-25), a presidential yacht in service from 1936 to 1945
* USNS Potomac (T-AO-150), an oiler in service from 1957 until destroyed in a fire in 1961
* USNS Potomac (T-AO-181), an oiler in service from 1976 to 1983
*USS Potomac (NCC-93093) Fleet Escort assigned to Exploration Foundation Fleet Command, currently under the command of Captain Z'Hai D'Snett.
...though not always glorious the history of my ships is honorable.
More ships with names to go through, now by character!
Berryshine Punch, Tac
USS Harmony - Odyssey class, science variant. Flagship of my main, with her T4 diplomacy and habit for trying to find a peaceful resolution before kicking someone in the face.
USS Lyra - Luna class RSV. Named mostly for the constellation
USS Ussuri - Caitain Atrox carrier. Named for an especially rare breed of cat from Russia, supposedly a natural hybrid of various small wildcats in the area.
Rafa Berrianus, Bajoran Eng
USS Jerrado - Defiant class. This character's a Bajoran, and I thought the name of one of their moons fitted.
Sh'Ress ch'Thiran, Andorian Eng
USS Resolute. - TOS Constitution class. I couldn't find a definitive list of the original Connie names (I have since, and Resolute isn't on there, but meh). There were three HMS Resolutes in the past, but the one with the most influence on the name was the second one, the flagship of the ships sent to find Sir John Franklin's, who had been looking for the North-West Passage. (The other ships in that fleet included both the Enterprise and Intrepid, at least during the first expedition.) During its second search for Franklin, the Resolute ended up getting stuck in the ice.
The reason any of that matters was A: The link with the Enterprise and Intrepid, both canon Constitution class ships, which, to me, made the Resolute fit in with them, and the whole ice thing. As the captain of the ship is an Andorian. (biography wise, my Resolute was an original 23rd century Constitution, contemporary to the Enterprise and, especially, the Intrepid. The Vulcans got their own ship, and, I reasoned, the Andorians would insist on one of their own. The Tellarites too, but in their case it'd probably be more because they wanted to join in the argument than wanted to keep up with the Vulcans)
USS Resolute NCC (numbers)-A -Odyssey Class Operations Cruiser. My Andorian spent levels 1 - 50 entirely on her TOS Connie, and I leveled her up doing missions and patrols - not sitting back and doffing my way up. It was painful, but ultimately satisfying. Once she hit 50, I decided to retire the old Constitution and ... well, she deserved to have her name kept alive.
Arrhae ir'Menae, Reman (well, alien) Tac
USS Nei'rrh - Defiant class. Names stolen unashamedly from the Rihannsu series of books which, btw, I recommend wholeheartedly. They predate TNG and were made definitely uncanon by it, but they're enjoyable. Plus, there's a horta ensign in them. I want a horta ensign.
The name itself is, of course, Romulan. Quoting from the little glossary in the back of the book, "nei'rrh - small birds, similar in size and flight characteristics to the Terran humming birds ... with a poison-secreting spur on the upper mandible of the beak. Also an insult, referring to a person annoying or dangerous out of all proportion to their size, status or (usually) worth."
"Dangerous out of all proportion to their size." - this sums up the Defiant class perfectly.
M'Tirr, Caitian Eng
USS Stalwart - Caitian Atrox Carrier. No cat related name or pun here. I looked into what we actually know about Caitians, and one thing that came up is that they are really, really big on loyalty. Stalwart seems to fit pretty well.
Meliss OEH-417719 Alien (in this case, sentient Orion Entertainment Hologram) (No, really) Sci
USS Zimmerman - Oracle class Deep Space Science Vessel. Named for, naturally, Lewis Zimmerman, inventor of the Emergency Medical Holograms and father of modern holography.
USS Deviant (NX-94205) - Tactical Escort Retrofit using Defiant variant and Belfast bridge.
Following a DS9 theme: the ship/registration, character (main), and his command crew (boffs) are all one letter/number deviations from the show's. Named it as such as a tribute to the awesome USS Defiant. Plus I didn't want to be silly with trying to fool the censor with 'Def1ant' or other silly variations that wouldn't cut it as an actual vessel name in the star trek universe.
Just incase you were wondering ...
USS Lexington (NX-91016)
USS Saratoga (NX-91060)
USS Ranger (NX-91061)
All three are Odyssey-class ships (Tactical, Science, and Operations, respectively). They all take their names after US aircraft carriers (and their registry numbers are based off their namesakes as well)
One of my characters is a Science Officer, who I started out in an NX Replica, which I named the USS Calnus. Calnus actually comes from the Star Ocean Franchise, with the ships bearing that name being Star Ocean's equivalent to the Enterprise.
Anyway, my Science Officer is now in a Rhode Island Nova, which is named the USS Calnus-A.
She'll be in that one until she hits Captain, where she'll get the Long-Range Science Vessel USS Calnus-B. And she'll stay in that until she hits Vice Admiral, where it'll be upgraded to a Long-Range Science Vessel Retrofit.
My vo'quv is the IKS EmostarQQlactica because Emostar Crylactica wouldn't fit. :p and the vo'quv looks way more like a battlestar than the catfish or the covenant corvette.
My b'rel is named after the princess in disney's atlantis.
On my eng, I named my negh'var IKS Prince Serg, from the wonderful Vorkosigan stories (nontrek scifi). I liked that the character, prince serg, was a horrible monster in private, but remembered as a hero in public. I think I was trying to suggest something about the duality of man, the jungian thing.
My vor'cha is named after the mad god in the old bard's tale games.
My starfleet klingon's ship is the USS Guy d'Haute Rive, named after the famous guillaume fontaine de la tour d'haute rive.
I have two identical Tac officers - one Fed, the other Klink. The Fed toons ships are all called Claw, and the Klink ships are all called Pach (which I believe is Klingon for Claw).
Where relevant, I name the ships after arachnids or flying insects, because that's the way I roll. My favourite ship name I have is probably for a Tac Escort Refit with a red line vertically dividing the hull/saucer called U.S.S. Redback.
(In Australia, our version of the Black Widow has a red stripe on her back, instead of an hourglass on her underside. Hence the nickname 'Redback' for the spider - and mine for the ship.)
I will never forget the day I bought the KDF Siege Ship, equipped the Reman Prototype Shields, and called it "Warspider". I nearly fanboied in my pants, and was a gibbering wreck for weeks. Some things are just so cool (to me at least) that they fry my brain.