"If you don't remember who you are, is it really still you?"
It may be better to flip that idea round - If one morning you wake up, glance in the mirror, and instead of yourself, see ... for example: Hillary Clinton, but you have all the memories of *your life* are you Hillary Clinton, or you?
"Much like people who have had brain damage and had their personality change completely. Do they even remember who they were before?"
"That does not mean that they 'are not'."
Are you talking about the physical them?
I suppose other people would have memory of who a person is, and project their view of them onto the "new" them, but for all mental identity purposes the person is different - will not react the same to identity based stimulae - you wouldn't recognise your own mother, and even physically speaking, despite the genetic identy, the physical us is constantly being replaced by the atoms in our food / environment, so how do you resolve physical identity? does our soul reside in our genes?
Two genetically / physically identical persons are still different because of their memories, so surely our identity (how we differenciate ourselves and others) cannot be based on the physical self?
How would you define the soul, mara? Would you say it defies explanaition, and just *is*?