What's that I hear you say? What happens if an old ship is preserved while there is another with the same name in commission? Like Enterprise A and her sucessors? Well, there is RW precedent for that too. In not too long there were be an RN Type 26 frigate called HMS Belfast. The preserved light cruiser is now HMS Belfast (1938) to avoid confusion. Plus it's not as if the Ford class USS Enterprise is CVN-65A, or CV-6B.
With the commissioning of the Excelsior refit class Enterprise, the preserved Constitution-class refit could easily have been designated USS Enterprise (2286).
I've also begun to think that maybe the prefix for Federation star ships should really be something like FSS, rather than USS. I also sort of wish that star ship names were a little less Amero-centric. Yes, there are some named after warships from other countries, but we don't see them all that often. But, that's just me wishing to see a few more iconic British names!