I saw one report that Cardinal O'Malley was also thinking of taking the name Francis if he was chosen. As a Franciscan (Capuchin) that would be natural.
There were two major Jesuit saints named Francis--Francis Xavier, who is better known, and Francis Borgia (a descendant of the Borgia pope, Alexander VI). Francis Borgia was a widower when he joined the Jesuits--one of his descendants became Queen of England (Catherine of Braganza, wife of King Charles II).
Francis Borgia was General of the Jesuits at the time of the evangelization of major parts of the New World.