Jye Leslie Schultz, from Dubbo, asked the court to issue a non-publication order that would prevent his name being made public by media outlets.

Video footage of Mr Schultz allegedly committing the act of animal cruelty sparked outrage when it was circulated on social media last month.

The footage allegedly showed Mr Shultz dragging the emu around and ripping its feather off while it was laying powerless on the ground.

A laughing bystander filmed the incident on the side of a road at Quambone, near Coonamble in the state's north west on June 9.

After community members contacted police, Mr was Schultz was arrested at his home on June 12.

He was charged with recklessly causing prolonged suffering to an animal and has not yet entered a plea.

In Dubbo Local Court on Monday Mr Schultz's solicitor Rachel Brown gave Magistrate Brian Van Zuylen a letter from Mr Schultz.

The court heard the letter contained allegations members of the Schultz family had been abused in the street and were fearful of going out in public because of the publicity the case has attracted.

Because of those allegations and media scrutiny, Mr Schultz asked the court to issue a non-publication order and police opposed the request on the basis it was in the public interest and consistent with the principle of open justice.

Magistrate Van Zuylen declined the request and allowed for Mr Schultz's name to be made public.

He said the court was "extremely concerned" at the way Mr Schultz and his family were allegedly being treated, but people who receive threats can and should report them to police.

The case returns to court September 4.