As he was baptized Joseph Ratzinger, Benedict XVI's patron is St. Joseph.
The Vatican statement reports: "This afternoon, shortly after 5:00 pm, Pope Francis called Pope Emeritus Benedict XVI on the telephone, to give him his best wishes on the occasion of the feast of Saint Joseph, his name day, and to express his gratitude and that of the Church for his service. The conversation was lengthy and cordial. The Pope Emeritus has followed intensely the events of these days and, in particular, this morning’s celebration, and assured his Successor of his continuous closeness in prayer."
With a Mass on Tuesday morning in St. Peter's Square, the pontificate of Francis was officially inaugurated.