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

To clarify, on http://ccle.ucla.edu 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.

In Moodle 1.7 there are default roles and those you choose to create. The process is a bit more involved than in older versions of Moodle. While in a specific course you would go to Administration > Assign roles. After clicking the role you want to add users to you are given the option of all users in the system in one column(on the right) and those users who are currently in the role you choose (on the left). You are also given the choice of overriding roles. The great thing about this, is you can decide what “Guests” can do in each class! There is no longer the blanket rules set by the program on “Guests.” This is a great thing for those professors who have complained about their “Guests” not being about to post to forums, etc.

Unlike version 1.6, there is separate administration for creating new roles. In 1.6 you would merely change the name of the role of the professor within the course. To define roles in the new version, starting at the site administration; Users > Permissions > Define Roles. When you click on the “Add a new role” you are given a huge list of options. So now you can create very specific combinations of rules. This is also where you delete those roles you don’t need. You can also decide what roles should be allowed to assign roles to others (Allow role assignments).

Moodle Links
Moodle Development: Roles
Roles and Capabilities Forum