Okay, I admit that this would have been more appropriate for St. Patrick's Day, but I missed the saint's day as I was distracted and busy.
St. Patrick was a Roman Britain who went by the name Patricius in his writings, which we would expect. Unknown, I suppose, to most moderns he left a short biography of his life. He came from an influential British family. Showing the extent of the remaining Roman world, his father's name was Calpurnius and his grandfather's name Potitus. His family was devout, with his father being a Catholic Deacon and his Grandfather a Catholic Priest. Before we get the "oh my gosh, a Priest who was married!" gasp, the rule prohibiting Latin Priest from marrying, which is a rule, not a dogma, had not yet been imposed, so that would hardly have been unusual. His father was also a decurion, a sort of Roman city councilman.
Patricius was not devout as a young man, but he became so when he was kidnapped by Irish raiders at age 16. He was a slave for six years, herding sheep for part of that time and becoming increasingly devout, until a voice told him to return home. Escaping and traveling 200 miles across Ireland he persuaded the captian of a ship to take him on board. He continued his religious studies and then travelled to what is now France to study them further, being ordained there. He then returned to Ireland to become the stout hearted evangelizer of the Irish.
Okay, what's that have to do with the title?
Well this, To St. Patrick, in his native tongue, his name wias Patricius. In Irish that became Pádraig. It doesn't even really sound like Patrick.
The Irish diminuitive of that is Páidín.
To the English, and hence to some Irish, Páidín sounds like "Paddy".
Paddy, not Patty.
Patty is some sort of English diminutive for Patricia.
Now, there are a lot of Patrick's and Patricia's in my family. Zillions. And occasionally somebody tries to affect an Irish accent and welcome us a "Happy St. Patty's Day", or say something foolish like "Patty me boy". Bah.
It's St. Patrick's Day, and if you are from a real Irish family, not one that simply puts on a button that says something foolish like "Kiss me, I'm Irish!" that is a Saints day. Not a day to wear green and drink green beer (and if you were Irish, you'd be drinking Guinness or Murphy's, not green Coors). And to the saint, he likely was called Patricius by his family and probably Pádraig by the Irish, who likely had a tough time with his Roman name. But nobody, I"m quite certain, called him Patty, ever, or Paddy, for that matter.
Patrick, fwiw, is the English version of Pádraig, because English came to dominate Ireland as the language during the long English occupation. The Irish name Pádraig never went away, but Patrick became quite common. But not in the diminutive.
And, fwiw, while there are Irish men who get tagged with the diminutive Páidín or Paddy, not all of them do by a long shot. In my heavily Irish family almost all the Patrick men end up being called "Pat". Some of the Patricia's end up being called Pat as well, and some end up being called Trisha.
But nobody is called Patty.