Err, the Enterprise has been a ship name for a few hundred years, quite a bit before Star Trek was ever conceived.
(Of course, both really come from a long lineage of naval vessels with the name.)
GP is referring to in-universe canon, where the NCC-1701 was conceived and constructed by Starfleet, long after the Space Shuttle program was obsolete.
Wikipedia articles are largely discouraged from using in-universe perspectives or content, as opposed to Fandom/Wikia/Memory Alpha.
We don't:
enterprise
entreprise
It's not "entrerprise" (that'd be an additional 'r').It's not totally unlike "center", which is "centre" in french and also "centre" in UK english (but pronounced "center", unless I'm mistaken).