Off the top of my head:
A fair while ago a different peak of Wildcat was thought to be the highest. I think there were already trails to both, and I don't recall whether signs on the peak state(d) elevations, so possibly no changes needed except to lists and guidebooks.
There are still several peaks where it's not obvious which bump is highest. Jefferson, Guyot... I assume somebody knows and cares but since their results are not widely published, it's hard to tell whether their answers have changed over time.
In some cases a name survives, but the mists of time cloud the history of which bump it applies to. Mt Lethe, a peak or two in the Ossipees, something about North(?) Carter, and at least one Nubble (the one below the Peak above the Nubble).
Sometimes the name moves through processes unrelated to improvements in measurement/mapmaking. The "Owl's Head" on the NH48 list is one example. Officially, "Owl's Head" refers to the bump on the southern end of the mountain (and/or its south cliff face). "Owl's Head Mountain" is an AMC coinage for the whole mass including the 4000' summit north of the original "Owl's Head". People naturally shorten the 4000' peak's name to "Owl's Head", but the "movement" of the name has nothing to do with any confusion about the height or location of the summit.
There was *also* a period of a few years when the (unofficial) trail ended a little short of the 4000' point on "Owl's Head Mountain" (there was even a cairn and a sign at the trail-end). That was purely a case of hikers (and self-appointed sign-makers) not being where they thought they were. The true summit had been found long before.