It is an anglicisation of the original Irish Mac Aodha, meaning literally "Son of Aodh".
It was traditionally written in English-language documents as Hugh, an unrelated name of Frankish origin.
The first bearers of the surname were the grandsons of Aodh (died 1033), who was son of Ruaidhrí mac Coscraigh, King of South Connacht.
[1] The surname's pronunciation in Irish has also given rise to the spelling McGagh (otherwise McGah or McGarr), forms of the surname which are geographically concentrated around the area of Belclare parish in County Galway, the centre of the Clann Cosgraigh territory ruled by the historical McHughs.
Other anglicised versions of the surname include Hughes and Hewson.