Catholics, what is the Pope's name (the current one who lives in the Vatican) and did he write this?

I don't know if he personally wrote it. His name (Joseph Ratzinger) is on it because it is a doent from the Congregation for the Doctrine of the Faith and, at the time, he was the prefect of the Congregation for the Doctrine of the Faith. Such a doent would not be considered his personal work.