Not sure whether you're looking for suggestions, but I feel like "Moral Kombat" could work as a title, since it's essentially the same thing as "Belief Battles" but phrased differently. And of course it's a pun on Mortal Kombat, although not a particularly original one; I know I've seen the same joke in a few different places (and I certainly didn't come up with it), although I can't remember where and I'm pretty sure it isn't the title of an existing game or anything.

Just throwing this out because the titles you've been suggesting, and that names the AI was throwing out here, reminded me of it.