What we appear to lose when our brains are damaged seems to have to do mainly with memory -- retrieving and storing them.  The personality seems to remain but of course cannot function well without the ability to remember things, or confusion and partial memories.  Eventually, when even short-term memory is lost,. even the personality seems to go, but it is hard to really make that assertion, and even then the elements of sentient existence -- experience of "qualia" -- the ability, for instance, to discern faces and colors and other sensations, to feel pain and hunger, and all the rest -- seems to remain.

This fits but of course does not imply the South Central Asian (Indian subcontinent) cultural idea of rebirth -- at death memories are lost but the personality goes on, not as a tangible thing but as a process.  The cultures of this area had no problem assigning sentience to animals, but not souls, which to the cultures involved was alien (the ideas are sometimes translated "souls," or "self," but this is a distortion.