Sasha: Clearly "dog boy" is a confused reference to a dog that urinates and so forth anywhere he wants. However, I have lived in the USA all my life and never heard the expression. If you ever have a conversation with me, and use the phrase "dog boy" I won't know what you are talking about, and neither will the rest of the population. That's the problem with attempts to learn something termed "English" from modern TV Situation Comedies. There is no absolute meaning to the phrase, "dog boy" although it is clearly a colloquialism the script writers for the TV program "The Big Bang Theory" have introduced. It means about as much as using an expression like "Cow Child" or "Cat Kid". ---Warm Regards, Bruce

Like Bruce says, "dog boy" is a term the writers made up for the show. It refers to a dog that urinates anywhere it wants and a boy that is not yet potty-trained.