Arthur, William (1857) An Etymological Dictionary of Family and Christian Names. New York: Sheldon, Blakeman. Public Domain.
WILLIAM
As described in historical dictionaries
An Etymological Dictionary of Family and Christian Names (1857)
From the Belgic Guild-helm, harnessed with a gilded helmet; or, as others say, from Welhelm, the shield or defense of many.
Patronymica Britannica (1860)
B UT WILLIAM. See Boutevilein.
Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.