I think there’s some of that, at some schools—Wharton being a prime example. hich it was after the building in wPenn is awfully selective all around these days, but there was a time not so very long ago when it was one of the less selective of the Ivies, and the Ivies as a group were less selective than they are today. But Wharton was more selective than other units at Penn, so there was a certain cachet in saying you went to Wharton rather than that you went to Penn Business School. But after a while it just becomes tradition. Wharton is probably still the more recognizable and prestigious name in some circles.
It’s a little bit similar with Stern, NYU’s business school, which is much more selective than most of NYU’s units—except Tisch, which you also hear a lot.
In other cases it’s more a matter of wannabe’s. Wharton is Wharton, Stern is Stern, Sloan is Sloan, so IU’s business school needs to be Kelley to put it in the same conversation. I think that’s largely a business school thing, though. You don’t hear it so much in other fields—some public policy schools named after famous public figures (Kennedy, Humphrey), some music conservatories or performing arts schools, but no one bothers to identify Columbia’s engineering school by its full name (the Fu Foundation School of Engineering and Applied Science). In the case of Boalt Hall, UC Berkeley’s law school, I’m pretty sure it was just named informally after the the building in which it was once housed, and the name stuck, even after it moved to a different building. But I don’t think the school has ever been officially named Boalt or Boalt Hall; that’s just a longstanding nickname.