The man faces a third charge of injuring a member of the public with a vehicle as he allegedly fled the scene of the shooting on Reynella Drive, Massey.
He first appeared in the Waitakere District Court the day after the alleged murder and the intense manhunt that led to his arrest.
Justice of the Peace Gerald Rowan granted an interim suppression order, preventing the Herald from publishing his name and occupation.
Both the Crown prosecutor David Johnstone and defence lawyer Mark Edgar sought the order - telling the court that identifying the man at that stage could affect the integrity of the ongoing police investigation, and fair trial rights.
There was a fear that evidence given witnesses to the alleged murder, attempted murder and dangerous driving may be affected if they were to see the man in the media.
The 30-year-old woman appeared in the District Court two days later and was also granted interim name suppression.
District Court Judge Brandt Shortland refused to grant suppression - despite her lawyer claiming she received a "barrage of threats" and was in danger.
Judge Shortland noted that, following police releasing her name and photograph while they were still trying to locate her after Hunt's death, her identity was "all over social media".
"Your name's been out there ... The reality is it's all over social media," he said.
"Like feathers in the wind, it's very difficult to put all those back."
Her lawyer immediately indicated she would appeal the decision - which means her name can not be reported for now.
Both defendants have been in custody since their arrests and they made their first appearance in the High Court at Auckland this morning before Justice Simon Moore.
They stood in the dock flanked and separated by security guards.
They did not speak during the hearing, but clasped their hands in front of them.
Police working on the case against the pair were in court for the hearing.
Edgar sought an extension to his client's name suppression, stating again that naming him publicly at this stage may impact fair trial rights.
Justice Moore set a trial date in July next year.
The trial is expected to take about three weeks.
The issue of name suppression for both the accused will be revisited next month.
The woman is also to seek bail then.
Both were remanded back into custody today.
