A judge ruled in September and reiterated last week that Dharun Ravi should have the name of the man who appeared in a web chat he viewed.
Ravi is charged with invasion of privacy and bias intimidation against the man and Tyler Clementi.
Clementi, who was Ravi's roommate at Rutgers, killed himself in September 2010, days after the alleged spying. His story sparked a national discussion about bullying of young gays.
Prosecutors and the man's lawyer say the defense shouldn't learn who he is now. The judge has given them until Thursday to appeal.