It was Cape Canaveral, then after Pres. John F. Kennedy was assasinated it was changed to Cape Kennedy to go along with Kennedy Space Center.
In the early 70's the name was changed back to Cape Canaveral by the Florida Legislature...the residents of the City of Cape Canaveral did not like that the name change had been forced on them so after 10 years of lobbying they were able to get the State to change it back.
KSC is comprised of the pads, which are on the Cape, and the vehicle processing facilities and Launch Control, which is on the north tip of Merritt Island...which is where I grew up.