Its a series of TV shows/films. How can a ship created for a an iteration of the show created in 2001 appear in earlier iterations? The NX-01 omissions in older versions of Star Trek has nothing to do with the E's time trip.
You appear to be getting "in-universe," and "out-universe" mixed up and combined. From a production point of view, obviously the NX-01 wasn't design when we first saw the legacy display. However, in-universe the NX-01 didn't appear among the legacy ships Decker and the Ilia-unit looked at in TMP, nor was the NX-01 present in the observation lounge wall in TNG series.
In-universe, something changed to place it there. If the NX-01, a ship with a prominent history (first this and that), wasn't present, it's not being initially named Enterprise could account for it's absence.
In the original history, Deanna never told Cochrane the Enterprise's name, because she wasn't there the first time through.