No way. This would be a complete insult to the USS Yorktown, her Captain, and its own illustrious history
So what? If the Captain feels offended, she's a goddamned traitor and will get booted out of the service and branded for life for being such a weenie.
ITRW, ships get renamed without much ado. Illustrious battleships get reduced to stowage hulks and are forced to donate their names to the newest best thing; there's no room for "getting offended" or other such sissy nonsense, not in reality.
That would imply that for 84 years, no other Starfleet vessel had the same experiences that the NX-01 had, and therefore, was not as “special.” I find that hard to believe.
The opposite could easily be true, though: quite possibly half a dozen other vessels did such splendid things that there was no demand for reusing "Enterprise" for a full century.
Timo Saloniemi