I remember reading a paperback book in the late 1970s or early 1980s that consisted, at least partly, of a series of thought experiments about identity. Examples were teleportation to another planet were the teleport machine broke and a copy was made on the distant planet, but the original survived, or, I think, brains in vats. I seem to remember that these were told as fiction, with a professor being the character that performed the various experiments. I started looking for the book again a few years ago believing it to be from Stanislaw Lem, but I searched through his titles and couldn't find exactly the book I remember. Maybe this description means something to someone who could help me?
The Mind's I came to my mind when I read your description. May be it is it.
It sounds similar to Stanislaw Lem's The Star Diaries (1971). The narrator, Ijon Tichy, isn't a professor but the collection is introduced by a Professor of Comparative Astrozoology.
I don't think it mentions teleportation but the first story has Tichy meeting and arguing with near-future versions of himself. In "The Fourteenth Voyage" he buys an electric brain. The next story has him swapping places with his future self and the one after that talks about souls in machines and autoevolution.
Though, I've never read it.
But I read his "Summa of Technologies", which includes descriptions of similar experiments. Unfortunately, I don't know if translation to English exist.
Rouge Moon? Unlikely that it is the book you're looking for, but it has some similarities to what you describe.