A Gauler or Waller, a foreigner, from the Anglo-Saxon "waller-went," foreign men, strangers.

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

WALLER. The A- Sax. iveallan means to spring up or boil ; and a ivcallere is one who boils — a boiler. At the present day i\\Q persons who rake the salt out of the leads at the salt-works at Nantwich-, are called n-allers. Halliwell. Hence the name was anciently latinized Salinator. In the North, a Waller is a builder of walls. The Italian surname Muratori, and the French Murier, correspond with the latter sense. H.R. Le Waller and Le Wallur.

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