Many faculty sites would list some students and many of those students are working or completed a thesis. Do faculty sites list also students who did an independent study?
I have only seen one professor who does list students who completed an independent study with him on his website.
However, it appears that he has a very specific goal in doing so. By looking at his website (and previously talking to him) it seems like he is trying to portray his strong motivation to instill students with real world skills by giving them projects similar to what they might work on in industry since a common critique of Computer Science programs is that they don't get students ready for industry jobs.
Other than that, I would say the norm is to only list students that you advise but there isn't a hard rule.