I would like to limit Group Members being displayed to regular users during group request to only see themselves during the request; while group owner would continue to see the full list of members. 

Our client requirements is that a regular user of a group should only see his/her user name in the members and not all members.  Is there a way for me to achieve this? 

Thanks. 

Provided there are no other requriements that interfere, you can restrict the visibility to all users for all users.

So you need to play with the MPRs and decide who can see who, in terms of users.  Member is just a reference to another user. If you cannot see that user, this may do.

THIS IS AN IDEA: