There is a huge tradition in philosophy thinking about these issues. The mind/body split is typically traced back to Descartes, who claimed that he could imagine losing a limb, and staying the same person, then maybe losing two limbs etc. up to the point he concluded the body was not a part of himself. Instead, he identified the self with an immaterial mind, indeed, somewhat like the perceiver of thoughts and impressions - (contra e.g. David Hume, who thought the self was nothing but the collection of such thoughts and impressions).
This radical split between the mind and the body has made its way into common ways of speaking and thinking, and accordingly, it is often tacitly assumed or presupposed in thinking about these issues. In the history of philosophical thought, the 20th century might be characterized as trying to overcome this long-established trend in thinking.
Currently, there is an interesting field in which phenomenology (a philosophical discipline) interacts with neuroscience to study the nature of the self. They take a lot of interest in schizophrenic patients, for many symptoms of schizophrenia can be taken to show a pathology of the self. Hence, the anomalous self-experience of schizophrenic patients is studied to elucidate the ‘normal’ structure of the self.
Now, concerning your question, it is important to first get clear about what is meant by this self, before we can turn to identifying it in this or thas location or experience. Many definitions have been proposed and the consensus in the literature is that there are some levels of self experience. In order to identify these one needs to unpack the levels, getting clear about what you are after. For instance, there is a notion of self that concerns the narrative we identify with. Which is made up of life-experiences, but also judgements of value, of what is important to us etc. This is a very elaborated notion of the self. Then, there is also what is dubbed a minimal self, which is particularly interesting in the context of schizophrenia. Such is said to consist of several aspects. The feeling that one typically experiences agency in thought and (other) motor action. This is disturbed in TI. Then there is a sense of ownership over experience, the feeling that it is you who is experiencing the experience - as opposed to someone else. This is tightly linked, but not identical to, a sense of psychological boundaries. The feeling that experience is private. This is disturbed in TB. Cognitive models have been proposed to account for these modes of experience (notably by Frith).
Now if such a minimal notion of self is considered, the question of how to identify with it becomes an interesting one. For these modes of experience are typically presupposed in normal experience. You may think of it as the form of experience rather than the content of it. As such, we do not infer them from experience to consciously construct a self and identify with it. The answer to how does one identify oneself is normally a moot question. The self is the subjective perspective that is presupposed in normal experience, constitutive of the very meaning of the notion of experience.
Yet, ofcourse, at least while psychotic, the very breakdown in the structure of self (and thus in the structure of experience) makes it a very relevant question, how does one identify oneself. For you can find (as I have) yourself sorting through intrusive thoughts, reflectively attributing them to yourself or not. And in delusions of alien control over the body, it becomes a very relevant question who is moving your arm, or even, whether the arm is really yours.
Thus it may seem that when psychotic, we have to reflectively reconstruct what is normally taken for granted. I’m not sure whether this is possible, but I did for a long time as you write, not identifying with the noise of hallucinations. But it is, from some perspective, clear that these are your thoughts. I tried to account for that by somewhat identifying with them in a metaphorical sense. That is to say that I tried to perceive of negative hallucinations as expressions of discomfort, and for positive ones as expressions of comfort or joy. In some sense, you know that the hallucinations are yours and produced by your brain - yet it doesn’t feel that way. You don’t experience them as yours. Whether you can reflectively re-establish this form of the experience is an open question to me.