Franciscan popes, none of whom took the name Francis

"They had it coming"

Franciscans*:
Pope Clement XIV (who suppressed the Jesuits)
Pope Nicholas IV
Pope Sixtus IV
Pope Sixtus V

Third order Franciscans
Pope Gregory X
Pope Pius IX
Pope Leo XIII
Pope St. Pius X
Blessed Pope John XXIII

via GOR

Yes, very thoughtful of Pope Francis and given that St. Francis is Italy’s patron it will have endeared him all the more to the Italians.

Then, showing he has a sense of humor he went on to relate how some Cardinals were suggesting other names to him. One said he should take ‘Adrian’. “Why Adrian?” he asked. “Because Pope Adrian VI was a great reformer.”

But another suggested he should choose ‘Clement’. “Why Clement?” he asked. “Well you could be Clement XV and have revenge on Clement XIV who suppressed the Jesuits!”

That brought roars of laughter from the assembled journalists - not least Fr. Lombardi who is also a Jesuit. In any case he does have another link to Pope Clement. Pope Clement XIV was a Franciscan…

Other interesting fact:

The Brothers and Sisters of Penance of St. Francis is a Third Order founded in 1996 by members of the Archdiocese of St. Paul in Minnesota. It was established for those who wanted to follow the original Rule of the Order, given by Pope Nicholas IV, as opposed to following the new Rule of Life established by the Third Order of St. Francis in 1990.

*Father Peter Fehlner, FI said there were six Franciscan popes, but this is all I found.