I can't imagine in the JJverse that starfleet would break the registry system for one ship, regardless of her captain's heroics. It should be enough that Kirk always gets the Enterprise, whether she's NCC-1701 or NCC-4580. Personally, I think those digits are getting old and it's kind of a stupid thing to do, especially considering the headache for the recordskeepers, what with reprogramming the system to allow dashes and letters and all.