Well to me it seems pretty obvious, that the "NX" denotes some kind of experimental vessel: In First Flight
there are the NX-Alpha and NX-Beta which clearly are experimental craft, analogous to Earthīs (real) X-planes. We donīt know how many (if any) followed after these two, but at some point Starfleet decided they had done enough testing and built the first "true" starship. Since it concluded this NX test series, they simply kept the NX-designation and added the numbers instead of the greek letters. And even though more than one NX-starship was built and they are comprising the "NX-class", they still remain experimental in that they are the first ships designed to employ warp-5-engines and perform long-term exploratory missions.
In later centuries (in-universe) they used NX-prefixes to again denote experimental vessels or to honor the NX-Class. Both of these can be true at different times