Of course the other familiar form for Patrick is Patsy, though I've never heard that used for the day or the saint. And it's not too common these days, I suppose because it sounds like its the female Patsy.

Patty instead of Paddy might be a mistake, or maybe a way to draw attention to the notice and therefore to the event.

( I never like St Paddy's as a name for the day either. It sounds Oirish.)