As described in historical dictionaries

Patronymica Britannica (1860)

BOOKE. Perhaps from the Fr. houc, a he-goat, with reference, possibly, to the beard of the first owner of the name. Barbe de houc is a phrase still in use to designate a small tuft of long hair under the chin.

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.