The lawyer indicated that his client wanted to appeal the decision, and the judge gave him an 11.30am deadline to file the appeal, otherwise the name's man would be free to be published.
No appeal was lodged.
A 31-year-old woman also appeared in court today, charged with conspiring with Carroll to assault Tucker and also with being an accessory after the fact to murder.
The 31-year-old woman was granted interim name suppression.
She was remanded in custody without plea to appear at Christchurch District Court on May 16.
The body of Mr Tucker, 36, was found dumped near Lake Ellesmere on Drain Rd, Doyleston on Anzac Day.
He was severely assaulted before his body was burned and then reportedly wrapped in some material, police say.
After yesterday's arrests, police conducted a scene examination at Carroll's Bishopdale home.
Police are also appealing for any sightings of a grey 1994 Nissan Cefiro travelling between Ruskin St, Addington, and Leeston on the evening of April 24 or the morning of April 25.
"These arrests have been the result of a hardworking and highly skilled team of investigators," said Detective Inspector Tom Fitzgerald.
"This has been a challenging inquiry, but my staff have worked tirelessly throughout the week to ensure the family of Mr Tucker have some answers.
"I'd also like to thank the community for their support and understanding so far. We've received an excellent response from them in terms of information throughout our investigation."
