A copy of you is you. Literally the atoms that make up 'you' are replaced all the time, by biology. And the atoms themselves aren't real. Like some models of physics suggest that physical things are constantly being copied and deleted already, like how objects in a cellular automaton universe are "destroyed" every time they move.
But how the universe actually works is irrelevant even. Other people can have a different definition of 'death'. If the information in my brain is preserved then that's all that matters to me. If I had to get my neurons replaced, one at a time, with 'artificial neurons' that would contain all the same information, then i would do it. Surely you would to. And you wouldn't even notice any change I bet. It wouldn't change anything observable at all. So how can it possibly matter?
But how the universe actually works is irrelevant even. Other people can have a different definition of 'death'. If the information in my brain is preserved then that's all that matters to me. If I had to get my neurons replaced, one at a time, with 'artificial neurons' that would contain all the same information, then i would do it. Surely you would to. And you wouldn't even notice any change I bet. It wouldn't change anything observable at all. So how can it possibly matter?