It used to be standard that when joining a (Catholic) religious order, the candidate chose a new name along with their vows. This was a form of putting the past behind, starting a new life, etc. Not sure about generic parish priests, but the members of assorted orders that I encountered decades ago - nuns, brothers, priests - all had names they picked on joining.
As part of the modernization of the church (Vatican II?) they seem to have departed from this centuries-old tradition, and many go with their real name. (Kings of England do it too now.) Popes, so far - not.