In order to hide this user from the directory, you will need to enable "allow users to remove their name from the online directory" under Profile Publish Access in Core.

For more information on Profile Publish Access view the Profile Publish Access Help Topic
Note: The steps below will temporarily enable all users to remove themselves from the directory if the Publish to Directories task is enabled in the All School role, so you should complete the next set of steps immediately after updating the test user's privacy settings, then immediately unmark the Allow users to remove their name from the online directory option again, if applicable.

To hide a user from the directory:
  1. Navigate to Core
  2. Select Security > Profile access 
  3. Choose Profile Publish Access
  4. Click Edit
  5. Mark "Allow users to remove their name from the online directory."
  6. Then, click Save in the upper-right hand corner
  7. Navigate to Core > People Finder > [user]
  8. Settings tab > mark Do not include my name or any information about me in the directory
Now that the user's settings have been updated, we need to readjust the Profile Publish Access so that other users cannot remove themselves from the directory
  1. Select Security > Profile Access again 
  2. Profile Publish Access > Edit
  3. Un-Mark the "Allow users to remove their name from the online directory." box
  4. Lastly, click Save
Directory changes do take 24 hours, but after that time the user will no longer show in the Directory.