Media companies are seeking the names.
Juror names are normally a matter of public record and judges must justify the decision to seal them, legal experts said.
The judge did, however, allow jurors to watch the Stanley Cup Final games last week, as the Pittsburgh Penguins beat the Nashville Predators, 4-2 - even though McCloskey, a huge Penguins fan, wound up missing the team's Cup victory parade.
In addition to bracing himself for a new criminal trial, Cosby is also battling civil cases, accusing him of sexual battery or defamation.
"It can never be clearer that if you speak up, you could be chilling the justice system in the future if jurors are needed in this case."
The search for jurors without any feelings on the case will only be more hard given the intense coverage of the first trial.
"I was ridiculously sick", when he found out about the mistrial.
Brian McMonagle, one of Cosby's lawyers, addressed the jury, "We came here looking for an acquittal but like that Rolling Stones song says, 'You can't always get what you want". Cosby was charged just days before the 12-year deadline for filing felony charges.
As an alternate juror, McCoskey listened to the six days of testimony with regular members of the panel, but was dismissed prior to deliberations. Including testimony from two women who accused the comedian of almost identical instances of drugging and sexual assault that allegedly happened years apart and on opposite sides of the nation.
He described the journey across the state of Pennsylvania as "the craziest, eeriest bus ride I've ever taken".
In new court documents, the prosecution asserted the court should withhold juror names to keep from compromising "an important right that will be prejudiced by publicity", such as the defendant's right to a fair trial.
During their deliberations, the jury asked to review the testimony of alleged victim Andrea Constand, particularly her testimony about the 2004 night the alleged assault took place, which produced over 300 pages of transcripts. Media organizations including The Associated Press urged a judge to release them, saying the public has an interest in "confirming that the outcome of the first trial was the result of an impartial process". And Mrs. Cosby's power is back. Cosby has vehemently argued against the allegations against him, claiming that any sexual contact he had with any of his accusers was consensual. Though the prosecution wanted to present testimony from 13 others who have said that the comedian drugged and/or violated them, the judge allowed the jury to hear from only one of them.
Former federal prosecutor David Weinstein said Cosby's celebrity nearly certainly played a role in the jury's deliberations, perhaps to convince "two or three jurors that it's impossible to convict Dr. Huxtable, to convict Fat Albert. that he couldn't have done this disgusting thing".