Anglo-Normans are so called because they’d lived in England for a hundred years (103 yrs) before coming into Ireland in 1169.
They were Vikings by origin who had become somewhat French while living and intermarrying in Normandy. They originally came from Norway or Denmark around 900. One of these Vikings was Rollo, ancestor of the Duke of Normandy.
The Normans had come to England as invaders with William, Duke of Normandy, in 1066, which was only a century and a half after the Vikings had settled in Normandy in 911.
In Ireland the Normans intermarried with the Irish and the Norman race was assimilated.
The first form of the name on record appears to be “Fanyn”.
The author of “The Norman People and their Existing Descendants in the British Dominions and the United States of America”, published by H.S.King in 1874, says that the names Fanning, Fannin and Fannon come from Fainent or Faineant and cite John and William Faitneant or Fainent of Normandy 1198.
The Irish conquest was an extension of the conquest of Wales – an activity of Norman lords in the marches who were acting more or less independently of the crown. Once successful, their conquests were adopted by Henry II.