You may find family members buried in neighboring rows. Conduct a search for your ancestor's family in 1850 or later U.S. Census records. Neighbors may be relatives as may any people living in the household listed with a different surname. Look at land records, especially for cases where someone sold land to your ancestors for a dollar or some other small consideration. The ones selling the land are likely to be the parents of your female ancestor.
Churches are a good source for birth or christening records which include the names of both parents.
Church marriage records will usually include the spouse's maiden name. If you have a possible set of parents for your female ancestor, search for their probate record or will. Surnames of female children along with the names of their spouses are often listed. Check newspapers for the locality where your ancestors lived for birth or marriage announcements or obituaries. Look for a death certificate.