They did but the people there wanted their name back (decades ago now), so now there's no such place as Cape Kennedy. There's Cape Canaveral, which is a small town just south of the Kennedy Space Center and there is also a Cape Canaveral Air Force Station which is used to launch some of the military rockets. There's also Port Canaveral which has cruise ships, fishing boats, and an occasional submarine.
Thanks to all who posted replies. I like the original name better ;)