The Pope, a.k.a Papa, Vicar of Christ, Vicar of Peter, Holy Father, Bishop of Rome, Servant of the servants of God, Supreme Pastor, His Holiness, The Rock, Supreme Pontiff, Father of Kings, Governor of the World, Successor of St. Peter, Shepherd of the Universal Church, etc.
Which ones did I miss?
His office is often referred to as the papacy.
Holy See and Apostolic See refer to the Pope’s ecclesiastical jurisdiction.
His authority in the Church has been passed down to him, in a direct line of succession, from the apostle Peter. Peter was given this authority to lead the Church by Jesus Christ:
“And I tell you, you are Peter, and on this rock I will build my Church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven’” (Matt. 16:18-19).
“When they had finished breakfast, Jesus said to Simon Peter, ‘Simon, son of John, do you love me more than these?’ He said to him, ‘Yes, Lord; you know that I love you.’ He said to him, ‘Feed my lambs.’ A second time he said to him, ‘Simon, son of John, do you love me?’ He said to him, ‘Yes, Lord; you know that I love you.’ He said to him, ‘Tend my sheep.’ He said to him the third time, ‘Simon, son of John, do you love me?’ Peter was grieved because he said to him the third time, ‘Do you love me?’ And he said to him, ‘Lord, you know that I love you.’ Jesus said to him, ‘Feed my sheep’” (John 21:15-17).
Note: It is important to remember that the Pope is especially revered by virtue of his apostolic authority and position in the Church as established and given by Jesus Christ. So any act of respect or title given to the Pope is done so directly out of respect and obedience to Christ and His work.