[WJ Miller]

On August 2 of 1945, the Canadian Armoured Corps was granted the prefix "Royal". Here is the initial roll of official "RCAC" units.
(note some were disbanded* by this time, but this list retroactively includes any units that served actively during the war):

The Royal Canadian Dragoons (1st Armoured Car Regiment)
The Lord Strathcona’s Horse (Royal Canadians) (2nd Canadian Armoured Regiment)
The Governor General’s Horse Guards (3rd Canadian Armoured Regiment)
IV Princess Louise Dragoon Guards (4th Canadian Armoured Regiment)
VIII Princess Louise’s New Brunswick Hussars (5th Canadian Armoured Regiment)
1st Hussars (6th Canadian Armoured Regiment)
17th Duke of York Royal Canadian Hussars (7th Canadian Armoured Reconnaissance Regiment)
14th Canadian Hussars (8th Canadian Armoured Reconnaissance Regiment)
British Columbia Dragoons (9th Canadian Armoured Regiment)
The Fort Garry Horse (10th Canadian Armoured Regiment)
The Ontario (Tank) Regiment (11th Canadian Armoured Regiment)
The Three Rivers Regiment (12th Canadian Armoured Regiment)
The Calgary (Tank) Regiment (14th Canadian Armoured Regiment)
12th Manitoba Dragoons (18th Canadian Armoured Car Regiment)
16th/22nd Saskatchewan Horse (20th Canadian Army Tank Regiment)
The Governor General’s Foot Guards (21st Canadian Armoured Regiment)
Canadian Grenadier Guards (22nd Canadian Armoured Regiment)
*The Halifax Rifles (23rd Canadian Army Tank Regiment)
*The Voltiguers de Quebec (24th Canadian Armoured Reconnaissance Regiment)
The Elgin Regiment (25th Canadian Armoured Delivery Regiment)
*The Grey & Simcoe Foresters (26th Canadian Army Tank Regiment)
The Sherbrooke Fusilier Regiment (CASF) (27th Canadian Armoured Regiment)
British Columbia Regiment (28th Canadian Armoured Regiment)
The South Alberta Regiment (29th Canadian Armoured Reconnaissance Regiment)
*The Essex Regiment (Tank) (30th Canadian Armoured Reconnaissance Regiment)
*31st (Alberta) Reconaissance Regiment (31st Canadian Armoured Reconnaissance Regiment)
*The Royal Montreal Regiment (32nd Canadian Armoured Reconnaissance Regiment)
*1st Canadian Armoured Carrier Regiment (not in the numbered sequence)