This feels like a political hit job carried out by the courts rather than the wheels of justice doing their thing.
The wheels of justice are doing their thing; the answer and legal reasoning is in the court transcript, as quoted and commented on by a news source: see Michael Cohen raid and first day in court. Transcript: 04/16/2018. The Rachel Maddow Show | MSNBC.
The overall argument made by the press lawyer - which convinced the judge and the court - is that if the third client's name is given to the court as sealed information, it should be public, according to the 1st Amendment and in the public interest.
(Transcript edited and condensed by me)
Mr. Balin: Your Honor, I apologize for interrupting. I`m a lawyer
representing the press. ABC, “The New York Times”, “Associated Press”,
CNN, and “Newsday”.
The judge says, quote: I think you'd better come to the podium.
Mr. Balin says, quote: I think I'd better too, your honor. I've sat
and listened until we got to the point where I realized there's a
public access issue here. Your honor, I'm Robert Balin from Davis
Wright Tremaine. Thank you very much.
...There is no credible claim that this client`s mere identity
is attorney-client privileged information. Michael Cohen makes the
argument that it would be embarrassing to be associated with what he
terms a raid at a house, in a home. Your Honor, I hardly need to
remind the court of the intense public interest in the issues that are
currently before this court. I look around and I see that every other
seat is occupied by a member of the press.
...That's the very nature of the First Amendment access right, so that
we the people and the press can monitor our institutions and have a
rational basis for agreeing or disagreeing...
...It was Justice Burger who I think put it well. People in our open
society do not demand infallibility from their institutions, but it is
difficult for them to accept what they are prohibited from observing.
That was in Richmond
Newspapers, Inc. v. Virginia many years ago.
...Your honor, I see no basis for denying public access. If your honor is
going to order disclosure of this name, I see no basis for denying
public access to that name.
Maddow's comments:
This is the lawyer for news organizations coming in and pressing this
point. The judge at this point has basically agreed that she's going
to take the name in a sealed envelope. The lawyer for the press comes
in and says, if you're going to take that name, there's no good
argument, there's no good legal precedent for keeping that name from
the public. The secret name of Michael Cohen`s secret third client in
his legal business, if that's going to be disclosed to the court, it
should be disclosed to the people.
And here is an interview with Balin where he explains the how and why of his arguments: Q&A: Lawyer behind Hannity revelation at Cohen hearing speaks - Columbia Journalism Review.
Other points:
Help me understand the public/private nature of courtroom findings,
requests as it pertains to this case.
Court proceedings are public; nearly everything that happens in a court is public information (aside from issues of national security as decided by panels of judges and/or grand juries; or issues of safety for individuals and/or witnesses who are party to the proceedings).
So far it seems like none little of the evidence has actually been
reviewed.
The nature and content of the evidence or its review has nothing to do with the identity of the clients. The issue is the secrecy of the client list, not the content of the relationship between the client and Cohen.