I had a little wander through Cockley Cley yesterday, en route to Oxburgh Hall, and here’s what The Concise Oxford Dictionary Of English Placenames had to say about it.
Cockley Cley, Norfolk. Claia in Domesday Book, Cochkleye in 1324. Clay, clayey soil. The additional Cockley is obscure, perhaps it is a plural noun meaning cock wood, wood frequented by wild birds.
And that is about as far as anyone else has got with working out the name origin. The Cockley bit might have been otherwise dropped over time, but there’s another Cley in Norfolk, so perhaps a differentiation made things easier.