I would guess that it could be a misconception borne of only having heard people say Paddy. I have observed that many American accents consistently pronounce a lot of the 't's within words as 'd's. This could make the distinction between Paddy and Patty impossible to determine if you had somehow not seen it written down or not paid attention to its spelling.
Also not knowing the origins of the name could help further reinforce this misconception due to the already mentioned lack of 'd's in the modern spelling.
Also not knowing the origins of the name could help further reinforce this misconception due to the already mentioned lack of 'd's in the modern spelling.