When & where was your grandmother born? If she was born prior to April 1940, she may be listed in an US census with her parents. A few states have open birth indexes. I assume that she is deceased, since you cannot ask her, and her death certificate would have her parents' names, if the informant knew their names. Her application for a social security number would also have her parents names. Baptismal records for infants include the name of at least one parent.
Dear Ms. Humphrey,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Population Schedules for the 1870 Census, the Population Schedules for the 1880 Census, the Population Schedules for the 1890 Census; the Population Schedules for the 1900 Census, and the Population Schedules for the 1910 Census, the Population Schedules for the 1920 Census, the Population Schedules for the 1930 Census, and the Population Schedules for the 1940 Census in the Records of the Bureau of the Census (Record Group 29) that may contain record of your grandmother living in the household of her parents. Some of these schedules have been digitized in part. The 1940 Census schedules are digitized and available using the Catalog. See NARA’s 1940 Census Records web page for more information. For access to the non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at email@example.com.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.
For information about the U.S. Census, see the Census Bureau technical documentation and questionnaires.
You may wish to search Ancestry.com for the U.S. Census. There may be a fee for using Ancestry. Instead, check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
For a copy of various vital records for your grandmother and her parents, we suggest that you contact the Office of Vital Records or the appropriate State archives or historical society for the state in which they resided.
We hope this is helpful. Best of luck with your family research!