I guess that would matter a great deal to me if I were in Ireland.
In the US we celebrate anglicized holidays with anglicized names and Americanized traditions, whether we should or not. It's cool on you to celebrate Padraig, okay. But if it's willfully ignorant to call St. Patrick's Day "Patty's" in America, it's also willfully ignorant use basically any English-language terminology for a religious holiday.
So the question is, do a bunch of drunk assholes really run around calling it "Paddy's" every year because they understand the etymological Irish roots of the holiday's name and have consciously chosen to ignore the American tradition of anglicizing everything? I doubt it.
You said "the Irish call it Lá Fhéile Pádraig", so I guess it does matter to you?
In Ireland we do understand the "etymological Irish roots of the holiday's name", because, you know, it's an Irish holiday. Also, as an Irishman I know that it's Paddy and not Patty, because Patrick is an Irish name. I don't know why you're arguing with me on this. You're American. You're wrong. It's Paddy.