Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
WOODROOF
As described in historical dictionaries
Patronymica Britannica (1860)
WOODROOF. WOODROOFFE. WOODROUGH. WOODROW. WOODRUFF. WOODROAFE. WOODRIFF. Apparentl}' corruptions of Wood-reeve, the reeve or bailiff who has charge of woodlands.