IMO, is a refit or new build and not the Yorktown. Makes more sense time-wise if the construction was already underway when the whale probe arrives.
Also, don't know if someone has mentioned it but it might not have been Starfleet that decided to rename the ship. Could have been the Federation Council that made the call. I like to think that the FC legislated in perpetuum
the whole Enterprise is NCC-1701-x thing as part of the "punitive reward" the crew gets. And so Starfleet can never change the association.