Adding my two cents, I've known two Patricks in my life. (I'm in the US.) One was a young man in his early twenties when I knew him, but that was back in the early 90s, so he'd be in his forties now. He was called
Patrick with no nickname. The other was an Irishman who'd moved to the US and owned an Irish bar. He was in his thirties when I knew him ten years ago. He also had no nickname--was always called
Patrick. No
Paddy for this Irishman---at least not here in the US. Maybe he had been called
Paddy in
Ireland, but since that's not a nickname thought of in the US it didn't take here. I don't know, but that occurred to me as a possibility.