This is assuming that genetics is what makes you the person you are. I’ve often thought about how staggeringly unlikely it was for the exact sperm and egg that created me to come together. But it’s somewhat less unlikely that a more generally similar situation would occur: that my parents would have a child (not necessarily from the same gametes as me, but around the same time and place) and raise that child the same way they raised me.
If personality comes from nurture, that less-unlikely child could still be said to be me; if personality comes from nature, then there’s only one egg-sperm combination that could have become the person I am. The reality is probably somewhere in between.