In the Middle Ages, the word -cock- was a generic term for a young man. It originally was used to applied to the young man who strutted proudly about (like the rooster), or was cock-sure of himself, but came to be applied to any young man who was self-assured, or a leader of his peers. As a result, it was applied to several names as a suffix that better-defined the youngish man by his personality. The name Wilcox is a compound name with the elements Will = pet form of William + cock = self-assured young man. Variations are Wilcock,
Wilcocke ; Patronymic forms are Wilcocks, Willcocks, Wilcox, Willcox, Willcockson , and Willcoxon.

Source:  Broken Arrow Publishing