"Grand Council Loyalists" is the historical term given to those who remained with the central government under Chairman Abdul Johnson. The members of this faction would have simply called themselves citizens of the Fed, as compared to their main opponents, which they called the Rebels.
This faction started by in 2238. As the Earth Federation began to recover after the 2nd Civil War, the multitude of political parties that existed after free elections were established. The Technocracy unified its allies into the Liberty Party. Soon a balance existed between them, the Tech Infantry veterans, and the corporations. In 2241, that balance was disrupted by the assassination attempt on Stephanie Harrington. This leads to a power struggle within the daughter corporations. The Technocracy, through their bureaucratic arm of Internal Security, reasserts control after general elections in 2242.
The Tech Infantry feared a return to the days of Technocracy rule. In order to prevent this, Marshal Sarah Dunmeyer attempts coup in late 2242 and fails. Half of the military joins with her to form the Tech Infantry Rebels faction. Despite the fact that they won the war, their leadership was decapitated by Rashid King's assassination of the Grand Council. Arthur Clarke is named the new Chairman of the Earth Federation afterwards, ending the war in 2244.