The man accused of the murder of Connor Morris will continue his bid to keep his name secret next week.

The 33-year-old West Auckland man's case was called in the High Court at Auckland earlier this month in front of Mr Morris's partner Millie Elder-Holmes, his family and a packed public gallery.

Justice Timothy Brewer declined name suppression for the defendant but his lawyer Marie Dyhrberg, QC, immediately indicated she would appeal the ruling.

The Court of Appeal confirmed the hearing for continued suppression would take place on Tuesday.

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Mr Morris' sister Cymmion has set up an online petition urging the courts to reveal the name of the alleged killer.

"It's important for the community to know who they should really fear and for the family to receive fair justice for Connor," the page says.

More than 14,000 people have signed up.

At the defendant's last appearance Ms Dyhrberg entered a not guilty plea on behalf of her client to the obvious disgust of the Morris family.

She asked for his name to be kept out from the public eye because of significant danger to him and his family.

However, Justice Brewer said most people in the community already knew the alleged killer's name.

The secrecy around the identity of the accused frustrated the Morris family, who stormed out of the High Court led by the victim's father Chris.

Mr Morris, 26, suffered a fatal head injury during a confrontation outside a party in the West Auckland suburb of Massey just over a month ago.

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He was held by Ms Elder-Holmes, his partner of six years, as he lay dying.

A four-week trial has been scheduled for August next year.