Try to think of it this way… if we had brain transplant technology and you swapped brains with someone so that your brain ended up in their body and their brain in your body… which one do you think would be you?

I’m not sure there’s any clear answer to this as it touches on so many known and unknown unknowns. But, the assertion is that there most people (especially in western intellectual traditions) would consider wherever their brain is to be them (see also the concept of “brain in a vat” etc). This may or may not be true for you specifically.

Neither? "Me" consists of both body and brain, so unless you could find an identical body somehow, neither resulting person would be "me".

I doubt that brain transplants will ever be possible, but in that hypothetical neither one would be me.

There are two of you now. And two of the other. There are tons of brain-like networks of cells in the body, no? In and around the heart and such and I'm certain we'll find more in the next few decades. The fun part begins in how capable either of you and the other will be in establishing a functional union.

What's gonna happen when "your brain" recognizes your old body in with another head? Will "it" get horny? Jealous? Angry? Happy?

Phantom pain and stuff like that comes to mind and the question of how many dimensions (not levels on scale) of consciousness there are in this physical world/reality ...

Only an ego would even ask this question

> All points in my body are equally part of 'me'.

That's a reasonable belief, but some people do not feel that way.

If I had my foot amputated am i still me? If i had my mind transplanted into a different body am I still me? etc. I doubt there are any good answers that are more logical than "I feel this to be true".

> I don't understand your reference to the western world

Some religions believe that people have a soul that is separate from the body, which contains a person's essence (And say, goes up to heaven when they die or otherwise continues on after death). Even among people who don't buy that, it sets the stage (even perhaps just subconciously) for other dualist beliefs where the body is separate from your "essence" (however you want to define that)