Is there any evidence Paul’s slave, Onesimus, mentioned in Philemon, later went on to become the Bishop?

Onesimus (Ὀνήσιμος) was a common name for slaves (transl. “a useful man”). There are two O. related to Paul in NT writings, one in Phlm 15 and another in Col 4:9. We know of at least four bishops and theologians named Onesimus: of Ephesos, of Byzantion, of Borea and of Sicily (died in the 3rd century). There’s no futher identification possible. We don’t know.