Tom or Tommy isn't going to be the key. It's how he is being raised and what kinds of responsibilities he is being taught. I think Ben Stein is doing this tongue in cheek, dont you? I bet he has a loving relationship with his son Tom/Tommy and it's nothing like he jokes about.
I think "Tommy" is perhaps indicative of "how he is being raised." He's being treated, still, as the baby, as the overly doted-upon only child. My concern is that he's not being taught many responsibilities. With a wealthy father, he may not have to work to earn any of his perqs. I don't know, and perhaps it's not my place to presume, but from this brief essay, at least, I get the impression that Tommy is spoiled rotten.
I do not think it is tongue in cheek. I believe Ben does have a loving relationship with Tommy, but perhaps not a parent-as-authority-deserving-of-respect-and-obedience relationship.