I had been told that Mulvey was not an Irish name,but I managed to get a history of the family name from Irelands Own magazine, this is what they said:
Mulvey is indeed an irish name anglicised from OMaoilmhiadhaigh which in turn derives from Miadhach meaning"Honourable" the 1st bearers of the name belonged to Co.Lietrim where they were of considerable importance and frequently mentioned in the Annals of the Four Masters and the Annals of Loch Ce. They are of the same stock as the MacRannals ( Reyonolds) and the O'Farrells and were cheifs of the Tellachebhellan and Muintir Eolais, in south west Letrim. There are another sept of O'Mulvey on the Atlantic coast of Co.Clare. They were called O Maoilmheadha.