U.S.S. Chilastra, the name of the first MMO server that I ever played on. I named it this in commemoration of the many friends I made there and in case anyone from that server came to STO they would know who I was.
My Ferengi tac now flies the USS Moral Bankruptcy. It made me nuts that its 1 letter too long and I had to spell it in one word, but still. He's a mercenary and works for everyone, no loyalties, no ethics.
My S31 Betazoid got command of the USS Sentinel, though I found it not too original. He's in Starfleet Intelligence, internal affairs, and 'watches the watchmen', so it was fitting. I also had the VNV Nation song in mind.
Cassiopeia is a constellation in the northern sky. It was one of the 48 constellations listed by the 2nd century Greek astronomer Ptolemy, and it remains one of the 88 modern constellations today. Cassiopeia is easily recognizable due to its distinctive 'W' shape formed by five bright stars. Cassiopeia A was first seen in 1680. In the sky Cassiopeia sits with Andromeda on the South side, Perseus on the South East and Cepheus to the North. She is opposite The Big Dipper, and can be seen the clearest in early November. In Greek mythology it was considered to represent the vain queen Cassiopeia, who boasted about her unrivaled beauty.
The name of my main character's previous ship's name, a light cruiser, was called the Sullivans after the destroyer of the same name. No reason for it, it was just something to fill the space.
The name of the current ship my main character flies is the USS Kumari, after the Andorian battle cruiser from the Enterprise series. I figured, at least in my personal game fiction, the name has seen continued use even after the the Andorian forces were merged into Starfleet, thus validating Shran's prediction that the Enterprise and Kumari names would be used on future ships. The Ushaan-class starship Kovac "captains" also seemed to fit the name.
I've also got plans to use other names names Grimlock (after the Transformers Dinobot of the same name, and for use on an Akira-class escort), Zea Dorsa (after a plain on Mars), and evantually, Kearsarge (after the Civil War sloop of war that engaged and defeated the Confederate raider Alabama). All of these ship's names were originally inttended to be used in a peice of fan fiction I was developing, but never wrote as I never manage to think of a story that would have satisfied me.
I also have an Andorian Engineering secondary character currently in a ship called the Monitor, after the Civil War ironclad of the same name. My intention, if I decide to play her out further, is to have her captain cruisers, all of which are named after famous warships of some kind.
T1 Shi'Kahr Variant - USS Cairo, now discharged, came from a Star Trek PBEmail Sim I was in years ago, now retired sim.
T1 Constitution - USS Vienna - name it came with, I liked it and left it.
Aurora Variant - USS Daybreak - took the Nova, Aurora, Quasar and put it through the Thesaurus and Daybreak was one of the names that came back that I thought sounded like a ship name I liked.
Horizon Variant - USS Odym - she has pieces of each of the three ships in that line and when thinking of Hope I thought of the Blue Lanterns who wield the blue power of hope (Green Lantern Comics) and their home planet on Odym.
Discovery Variant - USS Impulse - from a Star Trek PBEmail Sim I still play to this day. My character is even the same general character, class, etc from that sim. Although in the sim the Impulse is Prometheus class and her registry starts with a 7 and isn't quite this far forward in time
Luna Variant - USS Einstein - based on the name of a fanfic ship I was working on years ago, long since abandoned. That ship was supposed to be fast, lots of weapons, and had similar lines to the Luna.
Destiny Variant - USS Darwin - that's the name I recommended for this tier when they had the T5 naming contest so I stuck with it.