kokomo
Yes, there actually was an island called "Kokomo" just like in the Beach Boys song. Today it's called "Sandals Cay" and is owned by Sandal's Resort. It sits in Montego Bay, Jamaica and holds only a few amenities and primarily caters to couples. It's this very tiny (2 and 1/2 acres) island that they are referring to in their song of the same name.
I heard the Beach Boys made up the name "Kokomo" for the song because they liked the way it sounded in the song.

No, it's a real island off the coast of Jamaica. It just got renamed by it's owners; a resort.