What is the name of the Boston woman rumored to be Mother Goose?

There are tales that the original Mother Goose was the wife of an Isaac Goose (sometimes thought to be named Vergoose or Vertigoose), either named Elizabeth Foster Goose (1665-1758) or Mary Goose (d. 1690, age 42) in Boston Massachusetts. There is no evidence to support these tales and some evidence for other origins of the name Mother Goose.