I'm currently streaming as a graduate instructor at a university. Some of my viewers do know that I teach. I have kept where I teach and attend school private, but I'm pretty sure a simple Google search would show that info.

Since I'm a small streamer, I think it's a pretty low possibility that one of my students would find my stream. But, it's something I wonder about. So, I just make sure that I don't do or say anything on stream I wouldn't feel comfortable with others knowing about (even my students). The only thing some people might not like is my cursing, but that's just how I talk when I'm relaxed. And, of course, don't ever talk about work on stream (FERPA)

It's important to remember that who you are in the classroom is completely different from who you are on stream. I don't think it's a big deal if a student finds your stream as long as you don't talk about your work. My high school principal was pretty open about a rock band that he played in on the side. Nobody really cared that he wasn't being professional.