There's always the possibility that teh Enterprise is the U.S.S. Sovereign. Perhaps the 1701-D took it's nosedive in Generations with (all things considered) relatively light casualties, and Starfleet suddenly found itself short one flagship and up one elite starship crew. So they took their biggest and fanciest ship at the time, the newly commissioned U.S.S. Sovereign, added one quick re-christening ceremony, and some serious diplomatic dancing to mollify whoever was supposed to take command of it (with huge bonus laughs if it was Jellico) and voila, one brand new flagship for the fleet.
Highly unlikely since Starfleet names its classes after the first ship of her class (and usually notes that as well, see Defiant NX-74205 dediaction plaque "first starship of her class") http://www.bolarus.de/sibs/pic/plake8.jpg