I agree that her name should not be Mayhew. I'm not even sure her name was Hannah.
I found a blog -- The following information is from the book, "History of Windham County" and is at the library at Willimantic, Connecticut.
William was born in 1585 in Soffolkshire, England. William married Hannah Mayhew, date unknown in England and they came to the US in 1630.
Only thing is I just checked both histories of Windham County and neither of them even mentions William Gager or anybody named Mayhew
A recent book "The Gager Family" by Edmund Gager. Gateway press 1985. pdf download
"I have been told that the name of William Gager ' s
wife was Hannah Mayhew , but I have never been able to
prove this information. It is my assumption that she
died in England, as did six of his other children . The
deaths of these children are recorded in the Parish
Records in Groton, England . Perhaps this great loss
that he suffered was another reason for his departure
from England . I can only assume that he thought that
things would be better in the New World."