> like a virus doesn't become part of me -- the immune system acts a biological discriminator between what is part of me, and what is not
But what about symbiotic organisms? What about your microbiome? Or the mitochondria, which began its existence as a separate organism? Or, they say our DNA includes many viruses that our ancestors contracted. A number of these things do stick with us and we sometimes even become totally dependent on them to function.
To pick one possible simple and broad definition from WP, "Identity is the set of qualities, beliefs, personality traits, appearance, or expressions that characterize a person or a group." -- you made it sound like that set is empty, which doesn't make sense to me. My identity is part of "I". Every being has an identity; it's not something you can get rid of?