Was she Roman Catholic?
Frequently between registering a birth, and baptising the child, the parents change their minds. In this case, it's a minor change -- especially if it was her baptismal name (adding the Mary).
I've come across numerous cases where a child's birth is registered with one name (or even NO name), and then the baptismal register shows a different name nothing even close to the registered name at birth, then the child is known through life and until death by another name again.
I don't know that it matters what order the forenames are placed, so long as they're there, and there is an explanation in the biography regards the difference.