Why should it "show up elsewhere in the series"? ENT has precious few graphics of fellow starships, and all such depicting NX type ships (to wit, this single one) show the USS identity. In comparison, graphics on Boomer ships feature the ECS prefix - is that an "error", too? After all, the letters ECS are to be found nowhere on the actual Fortunate hull.
Much of Star Trek comes about as a series of "errors". Once on screen, they become "features". Some may be awkward features, such as a character missing a rank pip or half his fake beard. But there's no a priori reason to oppose the feature that NX class ships have an USS prefix, or that Klingons fly Warbirds - or that the rare death penalty associated in the early 2250s with General Order 7 goes away and gets replaced by another rare death penalty associated in the late 2260s with General Order 4. All of those are in fact logical and expected parts of the Trek universe, and the opposite would be unexpected and in need of explaining.
Timo Saloniemi