But the lord of each world is conspiring with outside intelligences, so the Confederation takes a detailed memory scan of their best agent and imprints it on a convicted criminal heading into each of the worlds, to assassinate the reigning Lord on each world if possible and at least to discover information regarding the conspiracy.
The first chapter of each book relates a similar anecdote where the secret agent gets his mind scan, and then wakes up still thinking he is "him" -- and then realizing s/he is actually one of the duplicates, then having to deal with initial thoughts of inauthenticity and just being a copy. As expected, though, the same personality imprinted in a different body begins to have different experiences based on that body and its unique set of experiences from that point forward, so the source and his four "copies" begin to diverge in personality to some degree.
To answer your question, I don't see people as entirely identical once their physical proximity diverges and they begin undergoing unique experiences. Just the mere reality of me standing "here" and you standing "there" results in a different perspective, however slight, that continues to diverge as more tiny differences accumulate. This is why identical twins with the same genetic makeup can have unique identities and personality traits over time.
... I do share the same thoughts about teleportation, though, and it brings to the forefront what the "continuity of consciousness" would be if it exists. Technically it's the assembly of atoms that is unique, not the atoms themselves; so we could "reconstruct" someone if we had the tech to attempt that reconstruction, but our consciousness is proximity-anchored -- it typically exists within a physical body. Is it just a byproduct of the composition of that body or does it exist apart from the body? Would the consciousness I feel as "myself" transport to a duplicate of myself constructed somewhere else? It doesn't seem likely if consciousness is a byproduct. So the deconstruction of a body and reconstruction elsewhere is really just a human Xerox process; you'd be disintegrating yourself and creating a duplicate elsewhere that seems like you to everyone else, but the "you" that felt aware in this body is not really the "you" that is aware in that body. But that new "you" wouldn't even be able to tell because of continuity of memory. (One movie that explores this issue is Christopher Nolan's "The Prestige.")