Anonymous BuddyPress Social Network

I'm looking for help in how to go about in creating an anonymous social network via BuddyPress that allows for my members to interact with each other with no barriers to communication, form groups, share their experiences with each other without compromising their identities.

This is a social network for individuals in recovery from addictions who crave community but value their privacy.

Right now in BuddyPress, you can look up a member in a directory and it will show their First Name and Last Name and their member profile URL will be based on their name. Ideally would like for this to be based off of their anonymous nickname.

Your help would be appreciated!