I did think about that. If the Enterprise was the first experimental ship, NX-01, then the later Columbia as a production model should have been standard NCC-02.
But okay... say the whole bit NX thing is not about experimental vessels, NX is the class of the ship. Then what does the registry mean? Enterprise NX-01?
[vessel name] [ship class] [hull number]?
As in, USS Enterprise Constitution-1701?
USS Excelsior Excelsior-2000?
USS Enterprise Galaxy-1701-D?
We have seen Star Fleet use NX for experimental vessels before.
We haven't seen Star Fleet use class names as part of the ship's registry.