The Vengeance was likely first named USS Excelsior, it had transwarp drive after all.
Different timeline, so highly unlikely in both counts, IMHO. If that were indeed the case, I'd expect it would have be called the USS Excelsior, rather than the USS Vengeance - and transwarp would have been gone into in greater detail (and would have actually been mentioned, in-movie).
But neither were referenced in STID.
If ever there was
an Excelsior in the Into Darkness
timeline, I think this may have been it... (speculation of course, and possible spoilers):