Yes. The ships are officially stricken from the Navy list when made a museum, and the name is available again. For example, there is an active duty Virginia class nuclear submarine even though the battleship is a museum in Wilmington.
As a practical matter, though, the Big E was such a famous ship that they might not have named a replacement even though they could.
Sorry, poor editing on my tablet. I was referring to 2 versions of the USS North Carolina.