William Fitz Gilbert de Lancaster and the Lancaster name

One source found in Google Books, calls William the son of Gilbert de Montanis, later styled de Furness or de Furnesio by Henry II. It calls him baron. William was a knight, supposedly son of Gilbert of Furness. He was granted the right to change his name to Lancaster after the ascension of Henry II. There were no de Lancasters before that time. As to Gundred, there yet isn't any evidence linking her to William de Warrene with any certainty.