The notion of an object, in the human sense, doesn't have any solid relationship with the physical world. I hope we are agreed on this much. For some objects, there is a stronger correlation between the human concept and the physical world (i.e. you could find a formal definition that matches to some extent what I mean by a particular spoon), but for other objects in our minds there is nothing in the physical world that truly matches our understanding (the Atlantic Ocean, as an object separate from the Pacific Ocean, is not a physical object, it is just a human abstraction).
In particular, our notion of the identity of an object has no relationship with the physical world, as the Ship of Theseus shows. Our idea that objects "shatter" and "transform", so that if I break a glass the pieces are a different object than the glass; or if I mix of bowl of flower with water and roll it into a dough, the dough is a different object than the bowl of flour and the water - these are not physically definable notions.
When it comes to human identity, the identity perceived by myself, the same logic MUST apply, unless you believe in a soul. The fact that I can think of myself as the same identity as myself 2 seconds ago, or myself when I was a handful of cells in my mother's womb, is obviously an artifice of the human mind. There is no such continuity in the physical world.
And this has all been said from the perspective of classical physics. If you go into QM, where any notion of identity of particles would contradict the theory and observations of it, things really break down.