I'm sharing internet with someone and I don't want them to be able to see my computer. I checked his computer today and I was surprised to see that my computer name was under Networks. How do I remove myself from it or make it private so he won't be able to access it?

You can't remove yourself from the list (easily) but he shouldn't be able to connect to your computer and affect you in any way. If he can, let me know and find out how he does it if possible, there's plenty of ways to stop him.

Wait aren't you stealing your neighbour's wifi anyway?

can't you just turn off file sharing? You could join a different workgroup too.

Change the network to Public rather than Work or Home.

You may still be able to see theirs, but yours should be hidden.