Who can see the identity of a concealed candidate?

A candidate with the title [concealed] or the symbol of an eye with a slash is a concealed candidate. A concealed candidate is someone who has decided to keep his or her information anonymous. You can view an anonymized version of his or her matching profile.

District placement directors (DPDs) can only see a concealed candidate's name if (1) they are that candidate's assigned DPD, and/or (2) the candidate has "revealed" his or her identity in a particular search. 

A church can only see a concealed candidate's name if the candidate has decided to reveal his or her identity (after being requested to do so).