When I play the GalCivII game, I tend to name my custom ship classes after the actors. So there's been USS Shatner, USS Stewart, USS Brooks, etc. I start with the captains and work my way down. So the most advanced ships usually wind up being Kyles or Mayweathers.
USS Allegheny NCC-71965 Galaxy Class Named for the street of my previous home in Lexington, KY where I lived for six years (the longest I've ever lived anywhere).
Someone else had suggested naming one after Carl Sagan ... I'd like to second that, as well. Most in the spirit of exploration, which seems very STAR TREKKIE to me ..