McNally is an Irish surname.
Origins.
Mac an Fhailghigh.
McNally, McAnally, and particularly Nally, are anglicized forms of the '. The etymology of "Failgheach" is obscure but probably represents a Gaelicized form of Norman French "Le Poer", denoting a pauper or more likely a religious hermit. Of Cambro-Norman/Welsh origin, the Mayo MacNallys were a branch of the Barretts of Tirawley, County Mayo. 
Mac Conallaidh.
In Ireland the surname is strongly associated with Ulster and prevalent in counties Antrim, Armagh and especially Monaghan. In Ulster it originated in County Tyrone, and is the Anglicized form of 'son of Cú Allaidh'; a Gaelic name of the Cenél nEógain clan meaning the 'wild hound', i.e. 'wolf'. (Not to be confused with Mac Con Uladh "son of the hound of Ulster") This McNally family is a branch of the “Northern Ó Néill” group of Ulster clans. They are separate from the Mayo name . 
References.
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 Surname listThis page lists people with the surname McNally. 