I don't think the Cyberdemon is Satan. The closest thing to Satan is the Icon Of Sin, in the last level of DooM 2. But I'm unsure if he actually is suppost to be "The Devil" or just some big ass demon.
What I'm having in my game is a total made up religion, based on these dudes with uber magic skillz that "became" gods. It's got the generic, good god, evil god, oh and get this, a neutral god!
Maybe you could do something like that, dooms. Or perhaps base it on Greek or Norse religion, perhaps.