Yes, it's a joke. His real name is Gerald King. :-)
I looked it up on snopes.com - no mention of his name ever having been "King".
Yearbook photos from Geraldo's high school and college (the University of Arizona) demonstrate that his name was not Jerry Rivers: his given name was indeed Gerald, and his surname alternated between the family name, Rivera, and his mother's "continentalized" spelling of it, Riviera.