The origin of Jenifer's unusual given name is unknown but it appears frequently in his family. His ancestors included great-grandfather Captain Daniel Jenifer (1637–1692/3) who was a loyalist sheriff in
Accomack County, Virginia, during
Bacon's Rebellion and who later moved to the
Eastern Shore of Maryland, grandfather Daniel of St. Thomas Jenifer (1672–1730), and father, Dr. Daniel Jenifer (c. 1699–1729). Daniel of St. Thomas Jenifer had a brother named Daniel Jenifer (1727–1795) who himself had two sons, one named Daniel of St. Thomas who died unmarried and one Dr. Daniel Jenifer (1756–1809). Dr. Daniel Jenifer in turn had sons named Daniel of St. Thomas (1789–1822) and Col.
Daniel Jenifer (1791–1855; congressman and ambassador). This Daniel Jenifer also had a son named Daniel and one named Daniel of St. Thomas (1814–1843).