The surname is an Anglicized form of the Gaelic name "Mac Donnchadha", which means son of Donnchadh or son of Donough.
Various unrelated clans carrying this surname existed in Ireland, at least two in Connacht: these MacDonnchadhas were a branch of the MacDermots, the kings of Moylurg.
Another McDonough clan were cadets of the O'Flaherty chiefs in Iar Connacht.
The second clan in Munster, whose chiefs held the Castle of Kanturk in County Cork, and who were known as the bards of Duhallow, were a branch of the MacCarthys going by McDonough.
Understandably then, various spellings of the surname McDonough were found in the many archives researched including MacDonough, McDonogh, and many more.