"some students use the courses as a stalking device" - probably goes beyond a technical solution such as hiding the course listing (as Gary mentioned you would need your site administrator to help with that anyway) and is, I think, an issue that you should take up with your college authorities re the potential stalking in the first place - whether Moodle allows a potential opportunity for such people to see what courses you have been on is probably only a tiny part of any solution to what may be a much wider problem!
General help
How do I hide my courses from my profile? [Student]
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