Justice Brewer said most of the community knew Murray's name and aggrieved members of the Morris family subsequently set up an online petition calling for the alleged killer's name to be revealed.
"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 15,000 people signed up, including Mr Morris' father Chris who stormed out of court when the defendant was originally granted suppression.
At the last hearing for Murray's case - which was held in his absence - Ms Dyhrberg entered a not guilty plea on behalf of her client.
She asked for his name to be kept out from the public eye because of significant danger to him and his family.
Justice Brewer suppressed details of Murray's location on remand, as well as details of his family; orders which still stand.
Mr Morris, 26, suffered a fatal head injury during a confrontation outside a party on August 3.
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.
