I just watched an episode in which he calls himself Ricardo...Ricardo y Acha, which must be correct, because "Enrique" means "Henry," not "Ricky" (i.e., Rick/Richard, "Ricardo," in Spanish).  Not sure if there is an episode in which he calls himself Enrique, but although it kind of sounds like Ricky, it's an entirely different name, so I doubt Desi Arnaz would have allowed such an error to be made.  In the episode in Hollywood in which Ricky forgets their anniversary date, he very clearly says Ricardo, which makes his name Ricardo Ricardo.  He also says "y Acha" (or spelled y Hacha?) not "y de..." but he may have been contracting it.