Can you hide student names in the Inbox?

johnson
Community Novice

In a course I can hide/disable the People tool if I don't want students see other students in People, but they can still see each other if they go to the Inbox and go to create a new message.  Is there a way to hide the students so other students don't know or can't see other students in a course?  We need this option for some remediation and probationary courses.