Dictionary of Family Names

ALCOCK, ALECOCK, ALLCOCK, ALCOCKSON.  A baptismal name meaning "the son of Allen," from the pet form Allicock or Allcock; v. Cock, and cf. Wilcock, Jeffcock, Simcock.   'The same holds one messuage which formerly belonged to Matilda Alcoke, doghtyr.'   'The same holds one tenement which formerly belonged to Alcoke of Hynganderode':  Rental of Halifax (1439), Cotton MSS. Vespasian; F. 15, Brit. Mus. 

Mr. Lower says this name is a diminutive of Hal, the nickname of Henry.  The evidence is against this view; v. Allkin.   There is clear proof that the original form was Alycock, and that this was abbreviated to Al-cock.   Allen would readily take the nickname.   Ally or Aly, and the suffix -cock was added as a matter of course.   The important point is to remember the enormous popularity of Allen in the 13th and 14th centuries, and the absolute certainty that both nickname and pet forms would be in everyday use.