The personality a person has when they drink or get drunk that is significantly different from their normal personality. This can be good or bad depending on the person/situation and level of intoxication.
Girl 1 : I saw you at the party with that guy you've been drooling over. How did THAT go ?
Girl 2 : Are you serious ? You saw him ! He was acting like a fucking idiot ! He had a drunkonality that made me want to have his ass kicked. It was SO embarrassing, I ended up ditching his ass !
Guy 1 : Hey that chic you were with last night was hot, man. Where did you meet her at ?
Guy 2 : Yeah, we work together. She has an awesome drunkonality too, we have a blast wherever we go kick it. She's cool as hell, I'm really liking this one.