Jason Charles, 47, of Roundhay Road, Harehills, died on December 20.
His death is not being treated as suspicious, West Yorkshire Police said.
It is understood that Mr Charles had a brother, called Joshua Charles, who was last known to have lived in Leicester.
However, the coroner’s office has been unable to trace him.
Anyone with information is asked to contact coroner’s officer Marie Silvester on 01924 292301.