Colonel Jack O'Neill wants to name the ship "Enterprise." This is a reference to Star Trek (1966) and its numerous spin-off television shows and movies, another science fiction show about space/time travel and meeting other species. Star Trek is referenced a few times throughout this series and its spin-off series.
Carter tells O'Neill they cannot name the X-303 the Enterprise but does not elaborate. In one sense, she is breaking the fourth wall as the implied reason is obvious to the viewer: different ship, different television show. At the same time, she could also be referring to the fact they are on a U.S. Air Force spacecraft (this series is set before the creation of the U.S. Space Force in 2019) so, given the rivalries between the branches of the U.S. military, a name with a strong Navy connection is out of the question. In the Star Trek (1966) franchise, Starfleet is based on the U.S. Navy and the starship Enterprise is named after the famous aircraft carrier.