Why would Cohen even comply with such an illegal order in the first place? He should have told Wood to pound sand.
Secondly. Hannity and others should now SUE Cohen for breaching lawyer/client privileges.
Note that Cohen’s political history is as a Democrat, until Candidate Trump. People don’t seem to have noticed that Hannity has become more conservative over time from his starting point as a NY Rockefeller Republican.
The client's name, by itself, is not subject to the attorney-client privilege, except in rare circumstances, which probably does not apply here.