Most of my alts I don't care much about, so I'll settle for aesthetics. Just hit random untill something 'appropriate' comes up and call it at that.
Mind you, appropriate doesn't have anything to do with special meaning regarding your captain or whatever. Captains getting to rechristen their own ships is a highly uncommon occurance. If you're given command of the USS Soggy Britches, the proper response is "Thank you sir/ma'am" and hope Klingons don't read English good. To give a ship a name to match the culture or traits of its captains therefor often feels unrealistic to me, unless it looks like the captain was chosen to match the ship's name, rather than the name to match the captain, which is probably why I've no trouble settling for the random namer in most cases.
That said, my Andorian (main) admiral commands the U.S.S. Salah ad-Din. That always struck me as a great name for a Sovereign class ship, to the point where I just had to have it in STO. I also always sort of took issue with Trek ship naming conventions. With very few exceptions, Starfleet ships always had American and Eurocentric names, despite there being more peoples on Earth, and about 150 more planets in the sky, and while it's not an alien name it's a step in the right direction I think. Makeup time and cost was an acceptable answer for the crews being mostly human, but hull markings really don't cost anything extra. And of course the name makes some small minority of people a little bit squeamish, and I won't deny that I always (no longer secretly) enjoyed that just maybe a little bit too much.
Before the Salah ad-Din, I had the same (main) captain (at the time) in a ship called the U.S.S. Thelian. Which sort of bent my own rule. It's an Andorian captain in an escort named for the last Andorian Federation president, Thelianaresth th'Vorothishria. Also a former starfleet captain. But I could see how, fresh out of Utopia Planitia, Starfleet might want to give such a ship to an Andorian, to score some bluey-points with his homeworld, so I made the exception. It's just one of those names. If they build a new U.S.S. Surak, the first CO is probably going to be a Vulcan too. Afterward, in both cases, it's who (or what)ever's next in line.
And of course, every new Klingon bird of prey is an automatic I.K.S. cha'bIp. (Then you count the lols and lames, and you know how many people in the zone can read at least some tlhIngan'Hol.)
I have a theme for my names (and a method for making NCC numbers but I won't go into that).
Currently I'm running through as a Tactical Officer, my current ship is the USS Nimble. All my ship names for this character (from this ship onward) are taken from Traits from Vampire: The Masquerade Laws of the Night. Because I'm going to be flying Escorts and the most famous one being the Defiant I thought that easily sounded like it could be a Trait from that game. Also I'm a roleplayer and loved V:TM back when I played it regularly (I've missed playing local LRP and Table top games doesn't happen as much these days as most of my group as moved away).
I'm probably not going to start another character till I either hit Admiral or till I finish the storylines, I haven't decided. But I do intend on trying out the other classes and some other races. For Science I'm probably going to go with a theme of Greek gods. For Engineering Probably Ancient Egyptian.
Oh also the starter ships are always deliberately off-theme, as you don't "choose" that ship it just doesn't feel like it is "mine" as much as the rest.
Named for a reptilian beast of burden in the Science Fantasy works of John Norman. It comes in a variety of shapes and sized from a four legged alligator type to the large Velociraptor War Tharlarion.
Also known as Gingie(In game) Sskald(Gates of Sto-vo-kor)
Well For me I have two ships that have a special name. My Sovereign is the USS Sherwood, named after the Sherwood forest. And my Defiant is the USS Nalbin, named after my characters home province on Bajor. As for my other ships, I pick names out of the StarFleet Technical Manual.
On the KDF side I pick something thats a joke and Translate it into Klingon. My Fav is the IKS Chocolate Tribble. (IKS yuch yiH ) although I just got my second B'rel and decided not to change its name.....IKS G'AG
My Fed ship is named, USS Casing Head. That is the name of the oil tanker my grandfather served in World War II. As my KDF, I hadn't really chose a name so its kinda random. Next time I get on the game I will create a better name for it.
I follow the One name -A, -B, -C convention. Find it to be easier for me than a whole bunch of names.
Under my FED eng toon (first toon) i figured I'd name my ship in memory of my father, who was just as much a trekkie as I am (he passed away in 2006 from complications from heart surgery), so the name "Son of Ramon" is applied to that toon (and its also my screen name if you didn't notice)
On my tac toon, I chose "San Lorenzo", because it is where I was born in Puerto Rico.
And on the KDF side... I threw caution to the four winds and decided to go on an aviary tangent... in Spanish. My raptor's named the IKS Po'llo Vi'ejo (my BoP is named IKS Po'llo N'ojado)...
The Redneck Academy Vice Admiral Dre'an M'illa - USS Newburg - Avenger Battle Cruiser / Vice Admiral Vivicius - RRW Gladiator - S'Golth Elachi Escort House of Wu-Tang - Lieutenant General Old Dertay Bassturd - I.K.S. N'ga - Mogh Battle Cruiser