A second shot police officer and a bystander struck by a vehicle during the incident remain in hospital.
The woman is charged with being an accessory after the fact to murder.
Court documents viewed by the Herald show she is accused of helping the alleged gunman as a driver "in order to enable him to avoid arrest".
Auckland's Crown solicitor Brian Dickey told the court today that the woman was located after the two police officers were shot following extensive police inquiries and calls for assistance to the public.
The accused's lawyer, Marie Taylor-Cyphers, made an application for interim name suppression for her client, whom she said was potentially in danger after a "barrage of threats" on social media.
It was also argued by naming the woman it would lead to the identification of the alleged gunman, who has interim name suppression.
Dickey opposed the application and said police publicly releasing the woman's name was justified to locate the defendant as quickly as possible.
Judge Shortland told the woman: "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" and declined to grant the suppression application in the midst of a "media frenzy".
However, Taylor-Cyphers immediately indicated she would appeal the decision - which means her name can not be reported for now.
The judge also suppressed certain details of the case.
He remanded the woman in custody until a High Court hearing on July 8.
Murder accused appeared in court on Saturday
The man accused of murdering Hunt appeared in the Waitākere District Court on Saturday.
The 24-year-old was granted interim name suppression and was remanded in custody until a hearing in the High Court on July 8.
He is also charged with attempted murder for allegedly shooting the second officer, and driving dangerously causing injury after a member of the public was injured after being hit by the car allegedly used in the getaway.
The names of the second officer shot and the injured member of the public have both been suppressed.