It's just one of those things you never stop and ask yourself. Is his name really Doc? Hell, Beyonce and J-Z named their kids Blue Ivy, Rumi, and Sir. With names, all bets are off. One would assume Rivers was born at a time when it wasn't as likely for his parents actually to name him Doc. But we've been calling him Doc that only a few people would know who Glenn Rivers is. Even fewer know how he became Doc.
Glenn Anton Rivers was the 31st pick in the 1983 NBA Draft. At that time, that made him the 7th pick of the 2nd round, and he was selected by the Atlanta Hawks. To give you perspective, Ralph Sampson, Clyde Drexler, Derek Harper, Byron Scott, and Dale Ellis were drafted in '83. Glenn Anton was drafted from Marquette University, where he played for three years and picked up his nickname.
While at a summer basketball camp at Marquette, then assistant coach Rick Majerus nicknamed him “Doc” because Rivers had worn a “Dr. J” t-shirt. The nickname instantly stuck and he's been Doc ever since. Well, Marc Zumoff, the 76ers play-by-play guy, has been calling him Glenn since his Boston days with a simple explanation. There's only one doc in Philly. Glenn agrees.
I have no idea where you rank Rivers on your current coaches list or whether he's a Hall of Fame guy. But there's one thing you can't take away from him - Rivers has always been smooth with fanbases and the media. The man knows how to work a room.