For example, I think if you'd have to explain how to change the string representation of some kind of object, saying "just define the 'str' method and then call it, like 'something.str()'" is simpler than "define a '__str__' method -- don't worry about all the underscores -- but then don't call it directly; instead of that, use the global 'str' function".
I don't know if that extra indirection (i.e. calling 'str', which, in turn, calls '__str__'; or 'next', that calls '__next__' in Python 3) adds more value than the simplicity of not having that extra indirection in the first place.
If it used normal names, Python couldn't evolve new methods for its protocols with language support. It would need some kind of annotation saying “yes I really mean to get this method called by the language and didn't just happen to use the same name by coincidence”.