If one took "Starship-class" like the British "Weapon-class destroyers" there was no HMS Weapon in that class. Just ships named after weapons. If Starfleet did something similar, they would have named all the new ships after famous starships from the last century, which would include the NX-01 Enterprise.
However there is also the tale of the Essex-class carriers, and their numerous subclass names over the decades. There are at least a half-dozen subclasses for those 24 ships, but after they were all decommissioned, they all reverted to "Essex-class". Constitution-class could be something similar. How they all started out, but as time and refits happened, there became a number of subclasses (Sombra, Constitution, Starship, Enterprise), but by the 24th century, they are just Constitution-class again in the records.