I’m kin with a character, but I have memories of being another character from the same canon. However, I’m pretty sure I’m not kin with them. Is there a name for having memories that aren’t yours?

As far as I’m aware, there’s not a word for this, but I think one would be really useful

Amnesia- meaning not remembering- is from the Greek, and so is cryptomneia (which means remembering things you didn’t know you knew.) 

Therefore, let’s draw on the Greek word for foreign (xeno) to create

Xenomnesia- remembering something that happened to someone else.