The family of alleged Bondi gunman Naveed Akram live in "constant fear" and have received death threats, a lawyer has told a Sydney court in a bid for their names to be suppressed.

The 24-year-old faces 59 charges over the 14 December attack on a Jewish festival, allegedly committed alongside his father Sajid, who died at the scene.

Akram's lawyer has asked for the names, addresses and places of work of his mother, brother and sister to be suppressed and removed from any previous coverage.

A magistrate last week granted a temporary suppression order while he considers the request, citing global interest in the case, but noted that the name of Akram's mother had already been widely published.

In the Downing Centre Local Court on Tuesday, Richard Wilson said the "outpouring of public grief, public outrage, and public anger" over the shooting - which killed 15 people and police say is the nation's worst terror attack - was "absolutely understandable".