Did you go with the default name for the ships you've got, or did you choose your own? If you did, why did you choose the names you have?
Tier 1: USS Agincourt (Named for the Battle of Agincourt in 1415 when the English trounced the French... again.)
Science Vessel: USS John Harrison -- The inventor of the Marine Chronometer that enabled accurate finding of longitude, critical for navigation. He was completely self-trained.
Cruiser: USS Endurance -- Named for the ship eventually crushed by the ice on Sir Ernest Shackleton's failed expedition to cross the Antarctic from 1912-1914. They all survived!
Escort: USS Hotspur -- Named for the fictional ship in Hornblower and the Hotspur. A sloop-of-war with 20 small guns. Fitting for a T2 escort.
Research Vessel: USS Kepler -- Johannes Kepler, astronomer.
Heavy Cruiser: USS Shackleton -- As named above.
Heavy Escort: USS Centurion -- A Roman army rank.
LRSV: USS Sagan -- After Carl Sagan
ECru: USS James Webb -- Another Astronomer.
TE: USS Resolution -- Looked at a list of British Navy ships-of-the-line and chose one I liked the sound of.
DSV: USS Palomar -- After the Palomar telescope.
Recon SV: USS Pathfinder -- Felt right for a Recon ship.
Assault Cruiser: USS Repulse -- Another British Navy vessel.
Star Cruiser: USS Amundsen -- Another Antarctic explorer.
Advanced Escort: USS Trafalgar -- After the huge battle during the Napoleonic Wars.
Fleet Escort: USS Audacious -- Another name I liked the sound of, a British ship.
I am not having much inspriation for ship names. I used the USS Kepler for my Science vessel, and the USS Quantum for Engineering, but both of those are only T1 ships. Unsure if I am going to stick with those names, try to find new ones, or just use the ones given.
I like the idea of sticking to the randomly generated ones, unless I have some name I absolutely have to have. After all, the officers don't usually get to choose the name of the ship they're being posted to, and most ships don't have names that relate to the captain's name in a hilarious fashion, nor are they <over the top awesome name that still sounds somehow generic>.
Although if I do get a terrible random name, I may click random again a time or two. A weakness, I suppose, but I try to control it.
EDIT: I feel like I should links to the names for people who don't recognize some of them. But then I realized I would sound like an ass. And then I realized I already sound like one. I probably shouldn't even put in this edit. . . Oh well, too late.
For now, I've only been going with the two names for my two primary characters.
USS Andromeda was picked before I knew about the paint patterning for ship design. Ironically, I didn't go with that scheme for it. The name is chosen for the Andromeda Galaxy, not 'Gene Roddenberry's Andromeda'. Essentially, I style that my character is an android from planet Mudd. And those androids were from the Andromeda Galaxy.
The other is the USS Ars Metallica, for a character in a 'starfleet-less' story I was writing in the ST universe. I figured there was plenty of opportunity to tell a ship story about a crew and not have them be 'THE MAN' as it were. The Ars Metallica will be crewed by characters from that story.