She was named after his father and grandfather, both admirals in the US Navy.
There is a reason the Senator is called John McCain the Third.
https://en.wikipedia.org/wiki/USS_Jo...cCain_(DDG-56)
Some afterthoughts edited in:
The US Navy generally does not name ships after people still alive (or still active?). In any event, if they were to name a ship after Sen. McCain, it is more likely to be a carrier - Carl Vinson got one for relentlessly supporting the Navy in Congress.