Since she is the only member of her species out in the galaxy and acts as a Sentinel and Exploring Ambassador, U.S.S. Sentinel seemed like a good name.
I've seen at least 2 or 3 USS Sentinels before I picked the name. It was what made me hestitate; I expected to see more. But in the end, it was the best option from my other ideas. Based on the background of the character, I also considered USS Nigh****ch (as a reference to Babylon 5), USS Sleep Dealer (reference to the movie as well as the all Vulcan crew with their nerve pinch) and USS Watchman (as reference to Watchmen, obviously).
Funny, I think every Ferengi has or had a USS Acquisition at a point. I know... well, one Ferengi without that name, lol My RA still has the USS Tongo Parlour, and might get a sister ship, USS Dom'Jot one day. My Ferengi tac had the USS Obscene Wealth and USS Eternal Greed before the USS Moral Bankruptcy. Still searching for good names for the T4 and 5 ships... I fear USS Grand Nagus Gint won't fit in. :-/
Before I even got the game, I knew my main ship had to be called 'Discovery' - just sounds 'right' for a Starfleet vessel, with similar connotations to 'Venture' and 'Voyager'. Plus, it's continuing the grand Starfleet tradtion of naming ships after early spacecraft, in this case the Shuttle Orbiter Discovery.
I really liked the look of the Excalibur class, and how nicely it combined the profile of the Constitution class and design elements from the Sovereign class, so that's what I went with for the ship - picked a suitably memorable (well, to me, anyway!) registry number, and I was good to go.
'Endeavour' sounded appropriate for my TOS-era Constitution - sounds similar to 'Enterprise', again, with the same connotations. As for the dedication, there's the Shuttle Endeavour, plus H.M.S. Endeavour, on which Captain Cook sailed on his first 'Voyage of Discovery' - both make suitable namesakes, methinks!
The registry number, 101700 is something of an 'easter egg' (or, at least, an attempt at one...). I wanted to have my Constitution with a 'canon' registry of 17XX (1786, for example) - unfortunately, the limits imposed by the game didn't permit that. '101700' looks close enough on the hull, as well as being i the right range for the STO era. Plus, the 'easter egg' is that it's a combination of the registries of the Constellation and Constitution (1017 and 1700, respectively) - the idea being that the number alludes to both, giving it a feel of 'authenticity' (again, in theory...! )
I toyed with both 'Eagle' and 'Resolute' for the name of my starting ship, before deciding that the latter would be better-suited for a Defiant class ship (can't wait to get one of those!). 'Eagle' is pretty obvious, named after the Lunar Landing Modules from the Apollo Program.
92526 was the starting registry, and that worked fine for me. However, when I first took command, it was configured as a Centaur class ship - can't stand that ship, as IMO it's just a kit-bash with mis-scaled parts and no secondary hull (where the hell's engineering going to go?!?). So, after an extensive 'refit' (basically transplanting the dedication plaque into a new ship!), the Eagle re-entered active service as a Miranda class ship...
...only to be mothballed almost immediately in favour of the Endeavour. Fate can be so cruel...
That's my mini armada at present - I'm already looking forward to adding Defiant/Prometheus class ships to the roster in due course...