IIRC, Popes started taking a new name when a man named Peter was elected. Not wanting to duplicate the name of the original Peter, he took another name.
Actually,it's a biblical tradition. God changed the name of all people he assigned special mission to, such as Abraham. Jesus, also changed the name of several of his disciples upon assigning them missions, such as St. Peter and St. Paul. It gave way to the tradition of Popes to change their name when they are elected as a successor to Peter.