The man accused of murdering Constable Matthew Hunt will continue to keep name suppression for now.

Hunt, 28, was allegedly murdered during a routine traffic stop on Reynella Drive in Massey on June 19.

A 24-year-old man is charged with murdering Hunt, attempting to murder another police officer and wounding a member of the public when he crashed his vehicle trying to evade a patrol car.

Police have also charged Natalie Bracken with being an accessory after the fact of Hunt's murder, assisting the accused killer by obtaining a car and driving him away from the scene.

Both have pleaded not guilty to their respective charges.

The man was granted interim name at his first appearance in the Waitakere District Court on June 20.

He sought to extend that suppression and was in the High Court at Auckland on Friday before Justice Geoffrey Venning to plead his case.

Ongoing suppression was opposed by the Herald.

He lost his bid for name suppression but was allowed to keep it until 4pm today in case an appeal was lodged.

The Herald can confirm that has been lodged so the suppression will continue until the appeal is determined.

Hunt, whose lifelong dream was to be a police officer, was farewelled at a funeral at Eden Park on July 9.

The other officer injured in the shooting spent several days in hospital but is now recovering at home.

He will remain off work for some time.

His name is suppressed, as is the name of the civilian who was injured.