Re: was NX01 ever referred to as 'The' Enterprise?
So there doesn't seem to be a fixed, universal rule. Some say the article should be used, some say it shouldn't. So that means neither "the Enterprise" or "Enterprise" is definitively wrong. Customs vary between different people and different times. Commercial ships take the definite article, but some naval veterans say their ships should never be referred to by the definite article while others say they do it all the time. Basically it seems to come down to a matter of preference, or what scans better in a particular sentence.
That's pretty complete.
A little wrench to add...
There is a Navy ship named "The Sullivans"...
Here we can have our cake and eat it too!
“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.