Why do they change their names when they become the pope?
It is to symbolize the continued apostolic succession from Peter, as Peter's name was changed when he was given authority over the church, the Popes also change their names when they are given authority over the church as Peter's successor.
They do not have to change their names but they do it as symbol of Jesus changing the name of Simon to Peter when He named him as the leader of His church and the first pope.
In general - the elected pope is welcome to take on the name of one he admires. His choice - period. Has nothing to do with anything more than that.