It was argued that Hannity's identity should not be revealed because it was "likely to be embarrassing or detrimental to the client". They, in a filing on Sunday night, made clear that they believe Cohen and Trump's lawyers should receive copies of the seized materials to make their own assessment of which documents are privileged.
Prosecutors with the USA attorney's office in Manhattan said they have a "filter team" of lawyers separate from those involved in the investigation in place to review the documents for any communications between Cohen and his clients.
But Judge Kimba Wood made one of the lawyers identify Hannity on Monday.
For Trump, it was the alleged $130,000 payoff of porn star Stormy Daniels in exchange for silence.
People familiar with the Michael Cohen probe have said he is being investigated for possible bank and wire fraud.
Cohen was in court for a hearing regarding the investigation into his business dealings.
They also said that Cohen appeared to have few clients other than the President and they had not uncovered any emails between the two suggesting the potential risk of violating attorney client privilege was slim.
Federal prosecutors in NY want a special "taint team" of government lawyers to begin reviewing files seized from Cohen during FBI raids last week, so they can decide which are protected by attorney-client privilege and which may be used to prosecute Cohen. Cohen has long described himself as an attorney for Trump but has for years filled a more wide-ranging role as a general troubleshooter. From 2007 to 2017, Cohen worked as a lawyer for Trump and the Trump Organization. We knew he also facilitated a $1.6 million payment to a Playmate who got pregnant during an affair with Elliott Broidy, the former deputy finance chair for the Republican National Committee.
Mr Cohen has admitted making a payment to the adult film actress, who claims the money was to keep her quiet about an affair she says she had with a married Mr Trump in 2006. He said Cohen reached out to him after being contacted by Keith Davidson, an attorney representing the woman, and said he retained Trump's lawyer "after he informed me about his prior relationship with Mr. Davidson".
It's unusual enough for federal agents to seize an attorney's records, and unprecedented to take those of a president's personal lawyer.
Under the procedure, the taint team would turn over to the case investigators all the material that is relevant and not covered by attorney-client privilege.
Cohen is asking for the review to be conducted by a court-appointed attorney.