As described in historical dictionaries

An Etymological Dictionary of Family and Christian Names (1857)

(origin: Local) From the town of Stanhope, in the bishopric of Durham, England. From stan, stone, and hope, the side of a hill, or low ground amid hills.

Arthur, William (1857) An Etymological Dictionary of Family and Christian Names. New York: Sheldon, Blakeman. Public Domain.


Patronymica Britannica (1860)

STANHOPE. The first recorded

Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.


BritishSurnames.uk is a Good Stuff website.