Who can do this: anyone who can edit the list.
Hide names, employers and other details from clients, so they can't go around you to the candidate.
Steps
Open the list and click List configuration > Candidate data control.
Under Candidate name, choose the Primary name clients see: Turn Secondary name on if you want a second line under it. Preview shows the result.
First name only (Tony)
First name + Last name initials (Tony S.)
Full name (Tony Stark)
Job title (Java Developer)
Initials only (T.S.)
Bullhorn ID
Under General info, turn Original CV / Resume and Candidate location on or off.
Under Work Experience, choose whether Employer name shows the Company name or only the Company type (for example "Marketing agency"). Turn Work location and Job description on or off.
Under Education and Certificates, turn Institution / School and its location on or off.
Click Save changes. Choose Apply to all existing candidates on this list, or Apply to newly added candidates only.
What happens next
Clients see the profiles with the hidden details removed. You still see everything.
Good to know
For the most anonymous profile: Job title as primary name, Original CV / Resume off, Employer name as Company type, Institution / School off.
The original CV usually has the name and contact details in it. Keep it off on anonymous lists.
You can change the settings for one candidate. See Hide or show data for one candidate.