Cooper's head office in Auckland's Newmarket was broken into last October and her entire 2021 spring and summer samples taken.
A 42-year-old man admitted to being the burglar this month.
However, others have also been charged with receiving the stolen couture, including a 45-year-old cake decorator.
She appeared in the High Court at Auckland with her defence counsel Christina Hallaway today to argue an appeal for continued name suppression.
Hallaway said her client was accused of receiving "a very small portion of clothing" and was concerned the cake retailer and her business - which was not currently trading - might face the scorn of social media if publicly identified.
The lawyer argued social media comments about the case may prejudice her client's trial by negatively influencing prospective jurors with ill-informed opinions.
When the cake retailer was arrested she was allegedly in possession of two jackets, a couple of dresses, and a suitcase full of Trelise Cooper clothing, the court heard.
While Justice Matthew Muir said he imagined the designer's items were expensive, he was satisfied the cake decorator had only "a small percentage of the total number of dresses stolen".
Earlier this month, the Auckland District Court was told that about 2000 garments, worth $750,000, were stolen - higher than the previously believed 1800 items valued at $500,000.
Today, the court was told the value may be as high as $870,000, as further clothing is recovered by police.
Crown prosecutor Pavee Patanasiri argued that the cake retailer had not reached the extreme hardship threshold required to keep her name a secret.
Cooper herself was also opposed to suppression continuing for the accused to help quell the baseless social media suspicions that her staff were involved in an "inside job".
Earlier, Judge Eddie Paul declined to continue suppression in the District Court, in part because of a desire to end the harmful social media rumours.
Justice Muir reserved his decision, but said it would be released promptly.
The 42-year-old man responsible for the break-in pleaded guilty to three charges, including burglary and a representative charge of obtaining by deception, and is due to be sentenced in September.
His application for continued name suppression was also dismissed by Judge Paul, with any appeal required by law to be filed by the end of next week. The man had earlier argued for suppression because he was "well-known" in the television industry.
The cake retailer and a 46-year-old florist, Andrea Nicole Edwards, continue to deny the allegations against them and are progressing towards a trial next year.
Edwards, whose name is recorded as Andrea Paul on her charging document, is accused of receiving the bulk of the stolen clothing - about $500,000 worth.
Hallaway said today there was a clear defence for her client and the case would proceed to trial.
A fourth person, a 26-year-old woman, was charged in May with allegedly receiving stolen Trelise Cooper-branded clothing.
The initial arrests came after police conducted a search of a property in central Auckland in November last year.
During the search, police said they recovered "a significant amount" of the clothing which was returned to Cooper.
However, in March the court heard about three-quarters of the missing clothing was still unaccounted for.
Speaking to The New Zealand Herald after the burglary, Cooper said access was gained into the styling room through a vent in an electrical room.