The oldest son of Sean and Claudia Finnerty of Staten Island, New York, is Jimmy Finnerty (but he's their second child, after Lily). Jimmy is something of a black sheep in the Finnerty family, (although it's usually no more than that he wanted to become a vegetarian, much to his parents' horror.) and he fancies himself a ladies' man in the schoolyard.
Jimmy Finnerty may have been named after a cousin of his father's. If so, that Jimmy Finnerty is probably the one who refers to himself in the third person (as in "Jimmy couldn't jump at all before he got these. Jimmy was like you."). "The Jimmy" sold odd-sized training shoes that forced the leg muscles to either adapt or die.
It seems like it's a pretty annoying habit, that referring to oneself in the third person. And that could be a very good reason why Sean and Claudia never invited him over to their house during any of the times when we were watching them.
'Grounded For Life' - entire series
'Seinfeld' - "The Jimmy"