From an Old English personal name, derived from wil ‘will, desire’ + mǣr ‘famous’. This died out in the Middle Ages, but gave rise to a surname before it did so. The modern given name is probably a transferred use of that surname, perhaps adopted in particular as a masculine form of Wilma.
Spanish: habitational name from Conteraras, a place in the province of Burgos. The place name is derived from Late Latin contraria ‘surrounding area’, ‘region’ (from the preposition contra ‘opposite’, ‘against’, ‘hard by’).