From Hall, Welsh, salt, and ham, a house or village, from its manufacture in that place, or being situated near the salt water. It may be derived from Hal or Hayle, a moor, and ham,--the house on the moor. Halham, the house on the hill, from Hal, Cornish British, a hill.

Arthur, William (1857) An Etymological Dictionary of Family and Christian Names. New York: Sheldon, Blakeman. Public Domain.

HALLAM. There are parishes so called in Derbyshire and Yorkshire, and that part of the West Riding of the latter county which contains the parishes of Shcflield and Ecclesfield is known as Hallamshire.

Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.