Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
STICK
As described in historical dictionaries
Patronymica Britannica (1860)
STICK. An Edinburgh surname. It may have been originally apjilied to a verger or staff-bearer, like ' Gold-stick,' ' Silver-stick,' &c.