I agree with flandry
, the Irish are mongrels. Saxon certainly isn't a common surname here, and almost certainly came here from England, but English settlers were common in Ireland for centuries and there was an eventual mingling of cultures that led to what is considered Irish today. By the mid-19th century, the traditional Irish tribes and clans weren't really an element or Irish society any more.
Just don't act like a plastic Paddy and we'll be cool.