The Miranda-class is named after the character of the same name from William Shakespear's The Tempest, so I took the name of another character from the same work. Not too original, but appropriate I felt.
Seriously... Saber-class, Rapier-class, Ushaan-class... I think they like blades. Not completely sure but, pretty darn. And so, the Saber-class U.S.S. Bayonet got its named.
The U.S.S Masamune was an Akira-class vessel already established in quasi-canon so I figured since this is an rpg, far be it from me to leave the other legendary katana out, and thus, the Akira-class U.S.S. Murasama was born...
Resistance is futile, eh? Well the the futility of my Defiant-class U.S.S. Resistance just blew your raggedy Borg Collective-asses in that cube the hell away! Hooah!
It was one of the only prominent figures in Greek mythology without a ship named after them according to both the Memory-Alpha and Memory-Beta wikis. Not really original, but I'm glad I'm using it now!
My current ship has a game-given name, USS Agamemnon, but my chosen name for my final ship is USS Eridanus, named after a lesser-known constellation. I believe the Eti Eridani sector is named for one of the stars in the constellation. The constellation is to the "right" of Orion in our winter night sky here on Earth.
It's a recon vessel that's used for commando insertions and special operations (and yes, I do use Boarding Shuttle I with it). Sensor Jamming and Trail Masking are its specialties. It also can act as a really nasty torpedo boat in a jam while offering decent support capabilities due to its elite crew: Science Teams and an Engineering Team. The name has been used for many British vessels during the Age of Sail and I just liked the ring of it. Cicero Harper, my main character, has a sort of 18th century naval look to him as well thanks to the muttonchops.
My advanced escort is the USS Shrike. It's named for a predatory bird and it's just plain got a nice ring to it. A character of mine in a tabletop RPG also shared this codename.
Then there's the Deep Space science ship, the USS Courser. A courser is a light hunting horse. The name might better fit an escort or a recon ship but it's one I've used for vessels from OtherSpace MUSH to SWG and in other settings as well. So no surprise it might crop up here in some form.
My Lucky 13 X name iss my gamertag(added 360 at the end recently to symbolize the console I play on mostly). But Lucky 13 X is itself a recognition of the ship name of my Explorer One character from Earh and Beyond's space MMO from EA. RIP.