Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
MILK
As described in historical dictionaries
Patronymica Britannica (1860)
MILK. " Certainly might be from Old Norse, mylJd, a rustic, one who milks. But upon the Avhole it is more probably a diminutive of Milo, Miley, Miles." Ferguson.