This surname is derived from an occupation. 'the oiler', i.e. an oilman. Farmore likely to be a form of Oliver, q.v.
Roberte Deane, oyiman, 1642: Reg. St. Mary Aldermary, London.
Bardsley, Charles Wareing Endell (1901) A Dictionary of English and Welsh Surnames, with special American instances. London, New York: H. Frowde. Public Domain