Whether you are looking forward from a females birth or trying to go backward to find their maiden name you have to realize one vital thing.
At marriage many change their last name to the last name of the husband. Pretty straightforward right?
I've found every variation on the theme with my own family. You may find in a census record that she wrote her maiden name only. Or on her death record that the record taker used her married name only. All I'm saying is that with females especially later in life you have to double check every variation if you're having trouble finding a record.
In order to find a mysterious maiden name I have only one thought. Attempt to trace the descendancy of the union. Because in the case of all her children their birth, marriage, AND death record have a chance at listing the maiden name of their mother. (the same applies for a mysterious place of birth)