Mr Marshall and the United Firefighters Union were unmasked on Friday as the applicants seeking to stop the release of the Operation Richmond report.
The operation, launched by the Independent Broad-based Anti-corruption Commission in 2019, investigated the Victorian government's negotiations with the union.
IBAC indicated the final report would be released to the public by July 1 but that plan was sidetracked by Mr Marshall and the union's Supreme Court injunction application filed in May.
At the May 22 hearing, Justice Claire Harris rejected their bid to have their identities kept secret through a pseudonym order.
She found there were insufficient reasons to grant the order given the information already in the public domain.
The judge granted a temporary pseudonym order to allow the two applicants to appeal her decision to the Victorian Court of Appeal.
But that appeal was rejected on Friday, with the court finding Justice Harris had not made an error.
"We are of the view that the decision to refuse the pseudonym order was plainly correct," the judgment released by Chief Justice Richard Niall and Justices David Beach and Peter Gray said.
"On no view of the material ... could it be said that pseudonym orders were necessary so as not to prejudice the administration of justice."
The court ordered their names be publicised and the applicants' barrister Paul Holdenson KC indicated he would not appeal to the High Court.
The Supreme Court subsequently confirmed the applicants were the United Firefighters Union of Australia and Mr Marshall, the union's national secretary.
A hearing over the release of the Operation Richmond report is still listed to be heard in the Supreme Court on June 24.
Outside the Victorian Labor party's annual state conference in May, Mr Marshall denied he was a plaintiff in the case.
But in a statement on Friday, he said he respected the appeal court's decision and would continue to fight the publication of the "unlawful" report.
"We have been restricted at law from commenting on Operation Richmond," he said.
"Examinations were in private, confidentiality notices were issued. The law still prohibits us from commenting on what is in the report and what it may say about us or anyone else.
"We will make a further statement when we can."
Operation Richmond investigated the Victorian government's negotiations with the United Firefighters Union.
They centred around reforms to merge Metropolitan Fire Brigade members and career Country Fire Authority firefighters into the new Fire Rescue Victoria.
There were reports Daniel Andrews, who was Victorian premier at the time of the negotiations, was questioned over Operation Richmond but he refused to confirm or deny that was the case.
The Victorian opposition plans to move legislation in parliament next week to write into law that corruption watchdog reports should be tabled "fast" and allow the government to stress such a requirement in court.
Shadow attorney-general James Newbury argued it would help deal with vexatious claims but acknowledged courts "could say no" on safety and constitutional grounds.
"Every Victorian is now feeling like they're being taken for mugs," he told reporters on Friday.
"Corruption is occurring and our chief integrity agency can't even release a report where presumably they make findings."
The Victorian government has been approached for comment.
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