Patty = Patricia, Paddy = Patrick. Unless St Patrick had a sex change and started going by "Patricia" by the end, he's not Patty.
If you were born in America, raised in America and live in America, you're American. If you were born in Ireland, raised in Ireland, or have lived long-term in Ireland, you might be Irish. That's kinda how nationality works.
If you were born in America, raised in America and live in America, you're American. If you were born in Ireland, raised in Ireland, or have lived long-term in Ireland, you might be Irish. That's kinda how nationality works.