He may or may not have changed his name to “Gerry Rivers” at some early point in his career. Kurt Vonnegut, Rivera’s former father-in-law, always insisted that Geraldo went by the name “Jerry Rivers” in the early 70’s and referred to him as such disparagingly to his dying day.
Snopes.com “debunks” the whole “Jerry Rivers” story, but Snopes is about as definitive and reliable as Wikipedia. It’s good for hit and run hyper-linking, but it’s not anything any serious person would hang his hat on. I’ve seen plenty of patently false assertions presented as fact on Snopes, almost always in the political realm (and always to the benefit of the left).
Bottom line: I have no idea if it’s true. But it’s a good nickname regardless.
I lived on Cape Cod when Rivers was married to and/or shacked up with Vonnegut’s daughter Becky(IIRC) over in W. Barnstable and knew people who claimed to shoot heroin with them. He was Jerry Rivers then, AFAIK.