I've heard different:
Vasquez is Vasco+ez. This may mean either '(son) of Vasco', or 'from Vasco', where Vasco means 'the Bask country'. A third origin of this surname is said to be occupational: 'sheppard'. see
http://genealogy.about.com/library/surnames/v/bl_name-VASQUEZ.htm or
http://home.att.net/~Alsosa/surnames.htm or again 'VÁSQUEZ
Son of Vasco, or one who came from the Basque country; one who tended sheep; a shepherd; dweller at the sign of the raven.' see
http://ivc.uidaho.edu/flesmethods/spanishsurnames.html