There are numerous surnames ending in -cock, some well-known like Hancock, Hitchcock and Babcock.
They are double diminutive personal names, formed from a pet form of a given name, usually Norman French, with the Middle English diminutive suffix -cok. For instance Hitchcock is from Hitch, a pet name for Richard.
However, i can't find any trace of a surname Didcock recorded, and I can't think what 'Did' would be a pet form of.