The Pope is the Bishop of Rome.  The bishop of the Diocese of Rome has, in the first place, the title of Bishop of Rome, the basis for all his other titles. Those officially listed for him in the Annuario Pontificio are:
Bishop of Rome, Vicar of Jesus Christ, Successor of the Prince of the Apostles, Supreme Pontiff of the Universal Church, Primate of Italy, Archbishop and Metropolitan of the Roman Province (also alternatively rendered as "Metropolitan Archbishop of the Province of Rome"), Sovereign of the Vatican City State.
Servant of the servants of God
He refers to himself as the Bishop of Rome. His primary title and is known universally by it or simply the Pope or Pope Francis.
Anyone who calls the Pope, Archbishop of Rome is trying to make a statement about something. Similarly RA never refers to cardinals as  Cardinal, e.g. ArchbFrancis for Cardinal George RIP,  lets hope he never has to name 6 or 7 or more cardinals.