Just a little pointer....
Many(esp in North America)who claim 'irish' ancestry,by which they think they are of Catholic Irish ancestry,are in fact of Scots or 'Scots-Irish'/'Ulster-Scots' ancestry.
Recent studies have shown that between 50 and 58% of 'irish' Americans are in fact of Protestant faith,and therefore of Ulster-Scots ancestry.
Millions who wave a tricolor every March 17th bedecked in green in fact should be frankly waving a Red Hand Of Ulster flag and wearing orange...
You are correct, especially with regard to self-identified Irish in the South and the lower Midwest. The Irish Catholics settled in the northern tier of states, with the highest concentration in southern New England. In a large Southern city like Dallas that has received many migrants from the Upper Midwest and the Northeast, you may find a common Irish name like Kelly and Murphy. If the first name is Irish sounding, like Sean or Patrick, or that of a Catholic saint, like Bernard or Francis, chances are that he is a Catholic, and in most cases, a Northerner. If his first name sounds typically Southern or generically American, like Lee or Dwight, he is probably a Protestant and a native Southerner.