OK let's have a closer look
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We do in fact have a very good idea of what constitutes our identity, and the largest portion includes our material characteristics ( gender, height, race, hair color, eye color, DNA coding, health, and other medical and visual properties ), paired with our personality ( the various psychological facets that manifest themselves when we are conscious ).
Together, these elements form a detailed profile ( all the way down to the molecular level ) from which any individual on the planet can be distinguished from another. When death occurs we certainly lose all physical identity, and even if some other invisible system can take over for the brain and body, then logically it still ends up being a copy of us rather than the original us.
Memory is only a fraction of who we are, but it is assumed by believers in things such as reincarnation to be sufficient to propose that a person who seems to have obtained a memory matching that of a deceased person, is then that deceased person, but in reality, even if such memory is able to be transferred from one person to another, that it is only a transference of a memory from one unique individual to another, not a transference of personhood.
Again, memory is only a fraction of who we are, and even if it is "conserved" in its original state, or for that matter, even if everything we are is considered information, and conserved in some buffer someplace, the result is still that such an information buffer constitutes a copy of our original selves at some moment in the past rather than our original selves in the moment. So again we run into the same problem. It seems that only way to truly live forever is for our original selves to remain intact.