Sometimes, the lack of the article "the" before Enterprise just felt wrong. When the characters said just "Enterprise" they didn't always say it in a smooth fashion, like they were consciously having to concentrate to not say "the."
As long as their manner of speech didn't make the lack of "the" awkward and noticeable, it works fine.
As long as their manner of speech didn't make the lack of "the" awkward and noticeable, it works fine.