In June, a coroner found the shooting of the 29-year-old, from Silverbridge, County Armagh, was not "necessary, reasonable or proportionate".
He stated his intention to name the soldier in a hearing on Tuesday when he concludes the case later this month.
Father-of-six Mr Thornton was shot in the head after his van backfired as it passed a police station.
The Parachute Regiment soldier, known as Soldier A, opened fire on the van believing the occupants had fired shots at the Springfield Road police station in August 1971.
The inquest into the unarmed labourer's death began in November 2015 and in his preliminary findings in May last year, the coroner said there were "other options available" to the soldier.
Mr Thornton's death sparked serious rioting.
Within days, 10 other people had been shot dead by the Army in a period the bereaved families refer to as the Ballymurphy Massacre.
In 2012, the government wrote a letter of apology to Mr Thornton's widow, Mary, confirming  her husband had been an "innocent man".

"Paramedics found the bodies of three people lying inside the aircraft," ER24 medical service told News24 website.
The plane crashed into shacks in Benoni, about 40km (25 miles) east of the city.
Footage on social media show emergency services taking bodies away from the crash site.
The BBC's Pumza Fihlani in the city says incidents like this are not common in South Africa.
The country has a very good record of air safety, she adds.
The now-deceased soldier who shot and killed Henry Thornton in Belfast in 1971 will be named, a coroner has said.
[NEXT_CONCEPT]
A light aircraft has crashed in the South African city of Johannesburg, killing all three people on board, emergency officials have said.