The organization of matter is constantly changing. If Heraclitus was right it’s hard to even say which organization of particles counts as Heraclitus.
"Wen considered the nature of time and understood that the universe is, instant by instant, recreated anew. Therefore, he understood, there is in truth no past, only a memory of the past. Blink your eyes, and the world you see next did not exist when you closed them. Therefore, he said, the only appropriate state of the mind is surprise. The only appropriate state of the heart is joy. The sky you see now, you have never seen before. The perfect moment is now. Be glad of it."
- Terry Pratchett
(from Thief of Time - a remarkable book, IMO)
* / Wen the eternally surprised
I think that's exactly right. For the general sanity of the human mind, we make and share assumptions about our experiences.
We don't really agree on what makes a person in the first place. When does a person begin? In the US, that's a heated debate. When does a person cease to exist? If you account for feelings, a relative with advanced dementia, or being in a coma indefinitely often doesn't feel like the same person. Or when people discover something really unpleasant about their significant other. A person only exist in a frame of reference. In a legal framework too, for example, which again changes from jurisdiction to jurisdiction.
Some cultures theorize an essence of sorts, that's unique per person, so it can carry the identity of a person. Let's call that a soul. This makes it easy to think about another person, as they can inhabit another body, or even an inanimate object or even share a body with another, and yet still be unique and addressable.