As described in historical dictionaries

An Etymological Dictionary of Family and Christian Names (1857)


(Danish.) Local. From stenet, stony, rocky.

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


Patronymica Britannica (1860)

STENNETT. A diminutive of Stephen.

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.