In that time of the early morning when the review of your life generally drives you from your bed do you really believe that your identity survives after all those years? What was I thinking of you ask yourself. If it's not the same I, if that I is an illusion not even operative in the present then what does the hot prickling sweat of embarrassment signify? Why should I take responsibility for that faux pas? Linking the concept of identity to memory as was done by John Locke is too easily dismissed.
This being premised, to find wherein personal identity consists, we must consider what person stands for; for which I think, is a thinking intelligent being, that has reason and reflection, and can consider itself as itself, the same thinking thing, in different times and places; which it does only by that consciousness which is inseparable from thinking, and, as it seems to me, essential to it; it being impossible for anyone to perceive without perceiving that he does perceive.(from An Essay Concerning Human Understanding II.28.9)
There are well known difficulties with this theory particularly when he adds further down:
......and as far as this consciousness can be extended backwards to any action or thought, so far reaches the identity of that person; it is the same self now it was then; and it is by the same self with this present one that now reflects on it, that this action was done.
Locke by the way is perfectly aware of the problems of forgetfulness and deep dreamless sleep which would create breaks in consciousness (cf. II.28.10) His proposal of serial substances with the same consciousness is an interesting one and is at least as intelligible as the claim that there is no such thing as a self.
An intuition of the connection between consciousness and identity that seems as firm as an anvil may be a very good place to start. Could memory taken in the Bergsonian way patch Locke's assumption of 'same' as in - same consciousness equals same man? Bergson maintained there is only ever a single consciousness with compresent elements that is constantly being rolled up in a single duration. It is this duration or memory working on a single moving point that establishes identity. Moreover this source of identity is most intensely felt as a contentless present moment. There is therefore no series of states as an ontological foundation. The series of states is a psychological construct that seems to underpin our identity. That part of Buddhism is right but that’s not all there is.