UPDATE TO MY ORIGINAL POST
As I’m trying to work my wat through the relationships in this family, I realized that the “3rd Mary” in the family might actually be a daughter-in-law as opposed to a second daughter named after the mother, Mary.
Mary 1 = Mother: Mary Burke (widow) born in Ireland immigrated to US in 1884/85
Mary 2 = Daugher: Mary Burke Murphy born in Ireland immigrated to US in 1887
Mary 3 = Daughter in law: Mary Burke Jr. (Widow) born in New York 1881.
Its most likely that the deceased husbands of Mary 1 and Mary 3 were father and son, Unknown Burke Sr and Unknown Burke Jr
*The answers I received about naming in multiple were very enlightening though!