The title of this article is conjectural as this subject has no known canonical name in the DCEU.
The Regime is an organization founded by Superman in a possible future, comprised of elite soldiers, and dedicated to maintaining his totalitarian Regime on Earth.
At some point in a possible future, Lois Lane would be killed, with Batman having been unable to prevent it. Superman, unhinged with grief, was left susceptible to Darkseid's Anti-Life equation and became a malevolent tyrant ruling the planet.  He presumably founded the Regime Soldiers to aid him in his totalitarian Regime of Earth, mercilessly killing anybody who opposes him. Batman promptly founded the Insurgency in order to combat this new threat, thus beginning the long Injustice War.
Injustice WarBatman, in desert clothing, exits a bunker, and watches his Insurgency allies approach. He meets with them and asks for the Kryptonite rock, the only remaining hope of defeating Superman. However, they open the box to reveal only green light bulbs. They apologize to him and hold Batman at gunpoint. He follows through with their commands as the undercover Regime Soldiers reveal themselves to Batman and the Insurgents. They execute them, as Batman watches helplessly. Angered, he begins a killing spree and guns down multiple stormtroopers, while helping some of his surviving Insurgents escape the area. Although he manages to take down most of the Regime Soldiers while Parademons invade the area and abduct many humans there, Batman is eventually overwhelmed by the remaining soldiers there who could barely restrain him. He snaps one of their necks, but then is brutally (but barely) beaten by the other stormtroopers. Seeing the damage that Batman was inflicting on the stormtroopers and their inability to restrain him, a Parademon knocks Batman unconscious.
Batman recuperates chained up in the bunker with his few remaining Insurgent allies, eyeing them helplessly. Superman himself then lands in the bunker, and his Regime Soldiers reverently kneel before their leader. He approaches Batman, swiftly murdering the other Insurgency members with his heat vision. Superman then unmasks the horrified and visibly scared vigilante. He expresses his anger at Bruce for letting "her" die, as she was "his world". Superman gives Batman one final sinister sneer, and ruthlessly kills him by tearing Batman's heart from his chest, thereby ending the Injustice War.
- Superman - Founder and Leader