Re: was NX01 ever referred to as 'The' Enterprise?
NX was the designation used for experimental starships in the Federation Starfleet. Earth's Starfleet obviously followed different rules.
Eh.... I think they just screwed it up.
Kind of like 1701-B, C, D, & E.
“We have to learn again that science without contact with experiments is an enterprise which is likely to go completely astray into imaginary conjecture.”
- Evolution of the Solar System, NASA 1976, H. Alfvén & G, Arrhenius, p. 257.