Actually, no, there are several US Navy ships named after living people. Its a fairly new thing, though.
"Traditionally, few ships of the United States Navy were named after a person who was alive at the time of the christening, but recently the number has increased; the list includes Carl Vinson, Hyman G. Rickover, Arleigh Burke, John C. Stennis, Bob Hope, Ronald Reagan, Nitze, Jimmy Carter, and George H. W. Bush. The Ronald Reagan was the first aircraft carrier to be named in honor of a living former president.[2]"
She is a fine ship, though. Can't help feeling a bit sorry for the crew of the USS Jimmy Carter.