I doubt very much there wiil be a USS Gray Davis. If there was, it would be under-powered!
And at least one ship, the U.S.S. Bozeman, was specifically named for one of the producers’ hometown.
You will, of course, remember this as the ship commanded by Captain Frasier Crane.
Not true. The ‘1701’ was the modelmakers home address.
- I’m trying to provide a cite for that comment but I’m not up to the task of wading through the bazillion and two Star Trek sites out there. About all I can offer you is the fact that I saw it explained on a show about a year ago. I remember being struct that the reason was so benign.
*Not that the ideas that float about on this topic aren’t funny to read about.
When that episode aired, the Captain’s name was actually Batesman. So he was Batesman on the Bozeman.
My friends and I speculated on if, when on shore leave, he was a boatman, a batsman, or a bass man. 
Close… it was Morgan Bateson.
I have to prove my nerdness here by providing some more useless facts.
Science vessels are generally named after scientists; medical ships are generally named after famous doctors and medical scientists (like the USS Pasteur).
Shuttlecraft are generally named after astronomers (the Galileo and the El-Baz) or physicists (the Feynman).
Runabouts, as noted above, are named after Earth rivers. This seems to be at the discretion of the captain; Captain Sisko is seen naming one in an episode of “Deep Space Nine.”
I believe the reason for the Earth-centric naming system is because almost all starships are constructed near Earth (in orbit around Mars).
I have another hypothesis, we are only seeing a small (Terran) portion of Starfleet. Wouldn’t it make sense that other member races would name their ships according to their customs ? Although I would have to note also the anglocentric tendency of ship names.