At issue during the hearing was Cohen's lawyers' request to be the first to read documents seized in a federal raid of their client's property last week citing attorney-client privilege between Cohen and his clients.
On Friday, District Judge Kimba Wood ordered Cohen's lawyers to produce a list of his clients by Monday's hearing so that communications protected by attorney-client privilege could be identified.
Cohen's lawyer's initially refused to identify Hannity as one of three people Cohen represented in an earlier court filing. Instead, only Trump and venture capitalist Eliot Broidy were listed. Broidy resigned as the Republican National Committee's deputy finance chair Friday after it came out that Cohen helped arrange Broidy's $1.6 million payment to a Playboy model in exchange for her silence about the affair.
The FBI raid of Cohen's home, office and hotel occurred upon referral by special counsel Robert Mueller. The New York Times reported the investigation did not appear to be directly tied to Mueller's investigation of allegations of collusion between Russia and Trump during the 2016 presidential campaign.
Wood ordered prosecutors to turn over materials seized form the raid to Cohen's attorneys to determine how much is subject to attorney-client privilege.
Cohen's lawyers may then share them with Trump and the Trump Organization.
Wood will then decide whether a separate team of government investigators or an appointed special master will review the documents before it can be used by prosecutors as evidence in the case.
Hannity said he and Cohen "have been friends a long time," in a Wall Street Journal report.
Cohen's attorneys said his work for all three of his clients was "more direct legal advice or dispute resolution -- more traditional legal tasks."
Attorneys for Cohen told CNBC that revealing clients other than Trump would likely be "embarrassing or detrimental to the client."
"As to the one unnamed legal client, we do not believe that Mr. Cohen should be asked to reveal the name or can permissibly do so," the lawyers added.
After ignoring an initial hearing last week, Wood said Cohen should make sure he was at the next hearing. Both Cohen and adult-film star Stormy Daniels, whose legal name is Stephanie Clifford, attended the hearing Monday.
In a separate case in California, Daniels' attorney Michael Avenatti filed an objection to Trump and Cohen's requests for a stay in her federal defamation lawsuit.
"Even if Mr. Cohen's Fifth Amendment rights were implicated, they have been waived. He has filed two separate declarations in this case addressing the facts with one of them being filed after the FBI raids. This is in addition to the myriad of public statements issued by Mr. Cohen, including a phone interview with Don Lemon of CNN occurring the day after the raids," Avenatti said.
Clifford is suing to be released from a non-disclosure agreement she signed on the eve of the 2016 election about an alleged affair with Trump back in 2006. Cohen arranged for the payment to be made and Trump told reporters last week he had no knowledge of it.
Information about the payout was among the items seized along with two cellphones and other business and tax documents.