An interesting thought, & yet I would also posit that most people are not the exact same person they were even 1 year ago. (No, I have no evidence or citations.) Some may consider themselves a different person from yesterday, though that may not happen every day. However, the same person as began reading your question? Yes, I would consider myself the same, as my following thoughts are things I have considered before.
I think it has less to do with cell regeneration/replacement as with experience. There is some evidence of "cell memory" (especially, examples with some people who've had