It was mentioned in several places such as "Mr. Scott's guide to the Enterprise" that the 1701-A was originally the Yorktown (or Tiho?) and was renamed Enterprise to reward Kirk for saving the Federation once again.
This is from Memory Alpha:
According to Gene Roddenberry, the NCC-1701-A was not a newly-constructed ship, but instead was the renamed USS Yorktown, a nod to the name of the starship in his original pitch for Star Trek. This was based on the fact that it was difficult to believe that Starfleet would build a whole new ship in such a short time, and then decommission it a short while after, and the early retirement of the Enterprise-A could be justified if the ship had been in service for many years under another name.
Mr. Scott's Guide to the Enterprise, released shortly after Star Trek IV: The Voyage Home, cites the origin of NCC-1701-A as the USS Ti-Ho (NCC-1798), an Enterprise-class starship which was a test bed for transwarp technology alongside the USS Excelsior. The Ti-Ho was rechristened Enterprise after Kirk and his crew were exonerated.
I think it was also called Levant as per Ships of the star fleet.