I also reckon that the English name for the bird was probably onomatopoeic, but as choughs disappeared from most of England (eg. in the 18th and 19th centuries) people no longer knew what the birds' calls were like and the pronunciation of the word 'chough' altered to that used now.
Incidentally, I once heard from a Cornish man that old people in that country referred to the species as 'chaw' which is a bit like the call, but coincidentally also rhymes with 'daw.'
The call of the chough is actually disyllabic, and that is reflected in the Manx Gaelic name 'caaig' and, I believe, also the names used in Irish and Scottish Gaelic, the other 2 Gaelic languages.
Allen