At his sentencing last November, the offender was discharged without conviction but also refused permanent name suppression by Judge Russell Collins.
It followed a plea deal mid-trial between the defence and prosecutors after the man stood before a jury charged with five counts of indecent assault, relating to two men and two women.
He ultimately pleaded guilty to two amended charges of assault under the Summary Offences Act. The assault charges were for the allegations against the two men, while the charges against the two women were dismissed.
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When arguing for permanent suppression for her client, Priest has said the man has suffered through an intense and highly publicised trial, while the negatively toned media frenzy vilified the man, tainting his character beyond repair.
She also said that despite the guilty pleas to assault charges, members of the public continue to label him a "sexual predator" and "the Labour Youth Camp pervert" on Facebook and Twitter.
In Justice Christian Whata's High Court decision dismissing Priest's first appeal, the judge accepted the reputational impact on the young man by publishing his name was "likely to be severe".
"He will likely become a target, not only for legitimate criticism, but for unfair vitriol and vilification as a sexual offender."
However, he ruled the effects did not meet the legal threshold for a permanent suppression order, nor did he think there was enough evidence to show the man will be ostracised.
Justice Whata also considered the ongoing public interest in the case because of the initial sexual allegations and connection to the Labour Party.
"The combined seriousness of the alleged offending and the political dimension strongly engages the principle of open justice," he said.
At the High Court appeal hearing in February, Justice Whata had signalled the prospect of continuing suppression until after New Zealand's general election.
But on reflection, he said in his decision, the political dimension precludes such a course.
When last August's trial began, the court heard there had been heavy drinking at the camp, which was described by witnesses as a "glorified piss-up".
Prime Minister Jacinda Ardern spoke at the event the day before the offending.
After the allegations came to light, Wellington lawyer Maria Austen conducted an external review of Labour Party procedures, which included several recommendations.
However, Ardern has said the report will not be publicly released while the court proceedings continue.
Former Labour Party president Nigel Haworth, who quit last September as separate sexual allegations within the Labour Party came to light, has said all the recommendations of the Austen report would be implemented.