For the entire time I watched 3rd Rock from the Sun, I never really thought about the names the aliens chose for themselves. They just seemed arbitrary. Well, Sally still does, but now, years later, it hit me that they were trying to pretend they were the same as every other Tom, Dick and Harry! - Sensei Le Roof
Mentioned in Alien Hunter:
Don: I just noticed that you're Tom, Dick and Harry.
Don: So, Tom, Dick and Harry. Like 'every Tom, Dick and Harry.'
Tommy: Well that doesn't mean it's a calculated attempt on our part to seem average.
There's a variation of that phrase that does indeed include Sally at the end.
An In-Universe example, from "World's Greatest Dick": Sally's expression when she accidentally discovers homosexuality, though she doesn't know what to call it, and realizes that Glenn was interested in her because he thought she was actually a man.
In "The Loud Soloman Family: A Dickumentary" Tommy claims that Dick beats him. Later on he also claims that he isn't Dick's real son, meanwhile Harry claims that he has a drining problem. Mary hears all this and doesn't know who Tommy's mother was, or indeed anything of of Dick's family history, so she must be thinking "What the hell happened to cause all this violence, drinking, resentment and secrecy? And why did Tommy keep all this to himself? Fortunately none of it is real.
Considering Tommy is older than Dick, his high school romances technically are incredibly dodgy...