Most "rebels" were simply TI troopers who stayed in their old unit.
"Tech Infantry Rebels" is the historical term given to those who broke with the central government under Chairman Abdul Johnson and created a new faction led by Sarah Dunmeyer. The members of this faction would have simply called themselves citizens of the Fed.
This faction started back in 2235 with the founding of the Populist Union, primarily filled by Tech Infantry veterans, although Fleet and LI veterans were welcome as well. As the Earth Federation began to recover after the 2nd Civil War, three power blocks formed out the mess of political parties. The "Rebels," the Technocracy (Liberty Party), and the Minority Coalition (Harrington daughter 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, reasserted 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 lost the war, their opponents' leadership was also 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.