"I understand if he doesn't want his name out there, but that's not enough under the law", Wood said, before ordering a lawyer for Cohen to disclose the name.
Adult film star Stormy Daniels arrived to watch a court hearing on Monday over documents seized from Donald Trump's long-time personal lawyer, in a federal investigation that could cast a harsh light on the president's business and personal dealings.
Hannity told The Wall Street Journal that he and Cohen "have been friends a long time". Cohen had argued that the documents seized were subject to attorney-client privilege, and the judge demanded that he list his clients so this claim could be evaluated.
On Sunday night, other lawyers representing Trump filed a letter to U.S. District Court Judge Kimba Wood, the judge overseeing the case, arguing that the president should be allowed to review the material before Justice Department lawyers.
The third is said to be Sean Hannity.
Over the last several months, Hannity has turned his primetime Fox News program into the most reliably pro-Trump show on any network.
"A lot of people here know his number", Smith said.
Cohen's legal team has been trying to seal evidence taken in the raids.
Failing that, they want the court to appoint an independent official known as a special master, a role typically filled by a lawyer, to go through the documents and electronic data seized under a warrant and decide what prosecutors can see.
President Trump's personal attorney Michael D. Cohen did work for Fox News commentator Sean Hannity in the previous year, one of just three legal clients Cohen represented after leaving his post as a counsel for Trump's private company in early 2017, his attorney told a federal judge Monday.
Hannity addressed the revelation of his name in court, telling listeners on his radio show on Monday that Cohen "never represented me in any matter" and that he occasionally sought Cohen's advice on legal matters. Former Republican National Committee deputy finance chairman Broidy's name surfaced earlier in the hearing as a second client of Cohen, Trump's longtime personal attorney who also is embroiled in the Stormy Daniels payoff scandal.
Mr Cohen did not respond to a request for comment. From 2007 to 2017, Cohen worked as a lawyer for Trump and the Trump Organization. Special Counsel Robert Mueller is separately examining possible ties between the Trump campaign and Russian interference in the 2016 election.
The president has called Mr Mueller's probe a "witch hunt" and denied any collusion.