Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
GREATHEAD
As described in historical dictionaries
Patronymica Britannica (1860)
GREATHEAD. Apparently from the personal peculiaritj'. Ilobt. Grosteste, the celebrated bishop of Lincoln, sometimes so Avrote his name.