Paddy, like Mick or Taig (Teague), has been used for centuries as an ethnic slur—a common form of disrespect referring to an entire body of people by a stereotypical name—but it’s not an insult if it’sactually your name. It depends on intent: shout my name at me with a brick attached and I’ll take it as an insult.
Irish Car Bomb isn’t a cute name for a drink or cupcake and, if you’re pushing shite like this, cut it out. People that lived their lives punctuated by car bombs aren’t amused. 25-year-old Ronan Kerr was murdered last year by an Irish car bomb; he can’t join you for a drink.