A carrier is a little over the top. The protocol used to be honoring individuals by naming destroyers after them. Lt Michael Murphy had one named for him. Miller has had a frigate named after him.
With carriers it used to be key battles in the nation's history, which is appropriate, then it was the navy's congressional benefactors, naval secretarys & presidents, which are not IMO, now its guys who fired machine guns.
Its ironic Miller is always honored for merely firing a gun on 12/7/41 when he should be remember for giving his life with all the others aboard the USS Liscombe Bay two years later.