The release came after Justice Thomas Warren turned down a request for a temporary restraining order to keep the names under wraps, CNN reported.
"If persons charged with crimes could withhold their identities, the public would not be able to monitor proceedings to observe whether justice has been done," the judge wrote.
A lawyer for one of the men argued that releasing client names would destroy the families and careers of good men.
The fitness instructor, 29-year-old Alexis Wright, is accused of having sex with dozens of men at her Zumba studio and videotaping many of the encounters.
Wright and her business partner, Mark Strong, 57, were arrested in July.
Since then police have been handing out summonses to those accused of soliciting a prostitute.