As an admin, you'll be able to adjust your gym's privacy settings. Settings include the ability to control the visibility of your members, your wods, and any of your gym activity from other BTWB users.
To edit your gym's privacy, click on the gym drop-down menu in the header, and then on the "edit privacy" link.
For the 3 controllable items, select either "everyone" or "gym members only". The "everyone" option will allow any user on the the site to view your information. The "gym members only" option will leave that information available only to people in your gym.
Your gym will automatically default to the "everyone" option, but you can change them at any time.