The general premise in the mind sciences is that there are different selves, somehow coordinated through the cortical midline structures. Plenty of different terms have been used, and hypotheses suggested, but the two "selves" I use for shorthand come from Daniel Gilbert: Socrates and the dog. Socrates is the narrative self, the dog is the experiencing self. If you want something a bit more technical, I suggest the lectures about well-being (lecture 3) here, and to get really technical, this paper on cognitive science exploring the self.