As described in historical dictionaries

An Etymological Dictionary of Family and Christian Names (1857)

An abbreviation of courteous. It may be from Curthose, a name given for wearing short hose, as the name Curtmantle was given to Henry the Second of England, from his introducing the fashion of wearing shorter mantles than had been previously used.

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


Patronymica Britannica (1860)

CURTIS. CURTEIS. CURTOYS.

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


Surname type: Nickname

Origin: English

Region of origin: British Isles

Country of origin: England

Religion of origin: Christian

Language of origin: English

BritishSurnames.uk is a Good Stuff website.