In Moodle can we make a site show up publicly, but not show its list of members?

To clarify, on why does Sysop not show members and Integration subgroup does?

The individual names listed under the course name are the Teachers you set for the course, not the students.

In Moodle 1.6 while in the specific course you can change the actual role name of the teacher to whatever you choose. To do this, choose Teachers (or whatever term you choose for Teachers) in the Administration block. After adding Teachers you can change the role name to Professor, TA, Reader, etc. You also can choose the order of the list of teachers. The options are 1 thru 8 and “Hide”. If you choose “Hide” then that particular teacher will not show up under the course name. You can choose to “Hide” all of the teachers.

If you want a way to list courses on the front page without the Teacher or Administrator listed with them, see below. One is with CSS, and the other is coming in Moodle 1.8.