It doesn't just raise questions about the self, but also lots of legal questions. Imagine you would transplant a brain in a different body. Who is that person now legally? Technically, only a single organ got transplanted, and everything else is still the body donor. But of course the person has the memories and presumably the sense of self of the brain donor. But the finger prints, iris scan and DNA of the body donor.
Of course we don't even know whether this sense of self is really purely attached to the brain. That brain is still connected to the rest of your body, and who knows what the body chemistry of the body donor will do to the new brain? Maybe we'll end up with a completely new person. Maybe not all memories will survive the transplant, but even if they do, you'll have a person who has the memories of the brain donor, but will be recognised by everybody as the body donor.
Mind you, if you transplant the entire head and not just the brain, this issue will lean a lot more strongly towards the head donor.
Of course we don't even know whether this sense of self is really purely attached to the brain. That brain is still connected to the rest of your body, and who knows what the body chemistry of the body donor will do to the new brain? Maybe we'll end up with a completely new person. Maybe not all memories will survive the transplant, but even if they do, you'll have a person who has the memories of the brain donor, but will be recognised by everybody as the body donor.
Mind you, if you transplant the entire head and not just the brain, this issue will lean a lot more strongly towards the head donor.