to go with a ship named USS archer, the runabout porthos
The runabout is good idea,
but the ships are named after past / deceased starfleet Captain's who made a difference in Starfleet.
, Captain of the NX-01 Enterprise, deceased in 2263
, Captain of the USS Enterprise, deceased in 2259
Captain Robert April
, Captain of the USS Enterprise, still alive.
, Captain of the USS Kelvin, deceased in 2233
Lieutenant Commander George Kirk
, XO of the USS Kelvin, deceased in 2233.
, Captain of the USS Constellation, deceased in 2267.
As for Paris, I'd have to make one up on the spot.
So ships named after the 24th century captain's: Picard, Janeway, and Sisko, would be in service during the late 25th century and I don't know if this line of ships would still be in service then.
Especially if Picard's grandfather was still in diapers, on mars.