It seems that, in a world populated by very real angels and demons, association with religions revolving around such creatures is frowned upon in Diablo III's world of Sanctuary. When Jon Bloodspray alerted me on Twitter that no characters could be named Atheist, I was ready to raise an eyebrow, but further testing indicates that you're out of luck if you're a believer, too.
Both Christian and Islam are also banned names, which is bad news if you're actually named Christian and wanted a character that represented you. Interestingly, I've found that you can name your character Muhammad, so you can at least portray the one religious figure guaranteed to piss people off. Allah be praised.
I've also found that you can have Scientology, furthering the organization's struggle to be recognized as more than a cult. You cannot have Mormon or Hindu, but you can have Buddhism. I don't suppose Buddhists are going to kick up much of a stink about that, to be honest. Naturally, Catholic is barred ... but Protestant strangely isn't. Clearly, Blizzard is picking sides.
So, what other religions can we get away with naming ourselves after in Diablo III? Feel free to experiment, and if you find anything of interest, let us know! After all, nothing's better than circumventing rules in a videogame for no other reason than pure petulance.