In answer to your question, "Mary’ is used not so much as a ‘last name’, but as a reminder that the Franciscans are dedicated to Mary, especially under the title of her Immaculate Conception.
St. Francis’ most favorite place in Assisi was the little chapel of Santa Maria degli Angeli (Our Lady of the Angels), also known as ‘The Portiuncula’. He had a great love of Our Lady, and exhorted his spiritual sons to have the same devotion.
Another Franciscan, Blessed John Duns Scotus, wrote much about the Immaculate Conception.
And, closer to our time, St. Maxmilian Kolbe called himself ‘The Knight of the Immaculata’, and wrote and spoke much of Consecration to Mary. On the calendar for his feast day of August 14, he is called ‘St. Maxmilian Maria’.