As an Irish-American New Yorker, I have to say that I never once have heard anyone call it St. Patty’s Day. It’s St. Paddy’s Day. If you called it anything else you’d look like an idiot.
Also Patricks of my aquantance in New York go by either Pat or Paddy, not Patty. In fact, an Italian friend of mine named Pasquale goes by Paddy.
This is one of those things that drives me to a rage, but I mostly shut my mouth because I don’t want to be “that guy.” Patty is a woman or burger meat.