I'm pretty sure no government or service renames ships during
their operation. I've heard of ships being renamed after selling them, or after having been captured, but never in the middle of its use
Far easier to think that the E-E was going to be named something else than to think the E-D was going to be renamed.
Frankly, I don't think the characters in-universe are as attached to the name Enterprise
as we, the fans, are. Why should Starfleet care what they call their best ship? The E-E could've been named USS Pansy
and it would've still been a top-of-the-line ship.