I think I agree with Samana Johann's answer, i.e. "conventionally" you give a name to a person, and say that, "the person named so-and-so was born in such a year, took their retirement 65 years later, and died in some other such a year."
Buddhism warns against having self-view, including e.g. "I am this body" or "this is my house". I think it gives at several reasons for that:
- SN 22.59 says something like, "the body is impermanent and you don't control it, so it's unworthy to be described as self"
- MN 22 says that sorrow etc arise from assuming any self-theory
- I think that later doctrines point out that things (everything), including anything like "body" etc. which you might be tempted to identify as "self", are "empty" instead of being (here I forget what term they use, but something like) "real" or "genuine" or "genuinely existent".
Nevertheless it's conventional to use "I" sometimes. "I" is the first word in this answer for example, for what that's worth, I often use it on this site to avoid speaking in a "this is the word of God" mode, i.e. to avoid e.g. making assertions such as, "Samana Johann's answer is correct", when I don't want to be that black-and-white about it. I also use words like "perhaps".
The parable of the chariot as explained to king Milinda says explicitly that such a thing as a named person is a "convention".
Buddhist doctrine describes or mentions the 5 skandhas and the 12 nidanas, and I think that's to explain what "really" exists instead of what people conventionally use to be self, e.g., "there isn't really 'me', instead what there really are are 5 skandhas, etc.", but I think those too are 'conventional' and empty.
SN 5.10 is maybe the earliest instance of the chariot allegory.
Then there's a doctrine of kamma ("I am the owner of my actions (kamma), heir to my actions, born of my actions, related through my actions") possibly to explain how past, present, and future are inter-related (the doctrine of the 12 nidanas is another description of that), but I think it does that without claiming that there's any identical or constant or eternal self.
When the Pali suttas say that it is not the "same" bundle of psycho-physical properties that is born and dies
Perhaps, if they did say such a thing, they might be saying something like that anything is dependently originated -- it exists because the conditions for its existence exist. And that the conditions at one time are different from the conditions at another time.
A baby exists depending on its parent, an old man doesn't, so baby and old man aren't the same.
That's true of the body but also true of perceptions, they're impermanent. Furthermore each perception is impermanent -- it doesn't exist, then it exists, then it doesn't exist, and then a different perception exists instead -- so it's not the same perception.
You might call it "a different bundle" in the same way that "grandfather's axe" or the "ship of theseus" isn't the same, though I don't know if that's Buddhist.