The 1850 through 1930 U. S. Census reports recorded the names of every member of the household. From 1880 forward, the relationship of each person to the head of household was also recorded. Look very closely at people in the household who have different surnames. An aged or widowed parent of the woman of the house may be living with the family, or they may have taken in a deceased brother’s child.
Example: The 1850 U.S. Census of Stewart County, Georgia, shows 21 year old Reason Jerkins and his new bride Mary (note that the married within the year columns is checked). My goal is to learn Mary's maiden name.
By 1860, Reason and Mary had moved to Mississippi; the 1860 and 1870 Census reports there record only themselves and their children in the household. But on the census of Hinds County, MS, we find that the now widowed Mary Jerkins has her widowed mother, Elizabeth Bates living with her.
If we look back at the 1850 Census of Stewart County, Georgia, we notice that the family recorded just above Reason and Mary Jerkins is that of William Bates, age 21 - of an age to be Mary's brother. And just before William, we find Elizabeth Bates who is likely the same Elizabeth Bates living with Mary Jerkins in 1880.