The 24-year-old has asked a court to suppress the names of his family members as well as their home and work addresses as he faces dozens of charges, including terrorism offences and multiple counts of murder.
A 10-year-old girl was among 15 people killed when Naveed and his father Sajid Akram, 50, opened fire from an elevated position during Hanukkah celebrations at Bondi Beach on December 14.
The elder Akram was killed by police after helping to carry out Australia's deadliest mass shooting since 1996's Port Arthur massacre.
On Monday, the 24-year-old's public defender barrister Richard Wilson SC sought suppression and non-publication orders over the identity of the alleged gunman's mother, sister and brother.
Akram did not appear from prison by audio-visual link during the hearing in Sydney's Downing Centre Local Court.
Mr Wilson acknowledged that the identity of Akram's mother had already been published.
"Hasn't the horse bolted on that?" magistrate Greg Grogin asked.
The application was based on protecting the mental and physical safety of the family members, the court was told.
"There is ... absolutely no reason why the relatives of the accused Naveed Akram should have their life put in the arena both within Sydney, NSW and ... now the world," Mr Grogin said.
An interim order preventing any publication of the three names is in place until Mr Grogin presides over a full hearing on March 17.
News Corp is seeking to block the proposed suppression order, sending its legal counsel Benjamin Regattieri to court to argue the publisher's case.
Mr Regattieri called the proposed orders futile, saying that extensive publication had already occurred in Australia and internationally.
Police allege Sajid and Naveed Akram acted alone and were not living at home at the time of the shooting.
After parking near a footbridge on Campbell Parade, the men allegedly tossed three pipe bombs filled with steel ball bearings and a tennis ball bomb into the Hanukkah celebration at Archer Park before opening fire.
None of the pipe bombs detonated, despite preliminary police analysis finding they were viable.
A box-like bomb was found in the boot of the car while two hand-painted ISIS flags were also in the vehicle.
A court suppression order allowing victims to choose if and when they go public with their story was also extended on Monday.
The attack triggered an outpouring of grief and a suite of legal changes addressing gun ownership and extremism as well as throwing a spotlight on rising anti-Semitism in Australia.
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