• The Exterminatus Squad: Evokes a sense of decisive, lethal action against monstrous threats.

• The Bio-Hazard Response Team (BHR): A more clinical, scientific approach to monster hunting, suggesting specialized training and equipment.

• The Anomaly Containment Unit (ACU): Implies a focus on containing and securing monstrous entities, rather than just eliminating them.

• The Xenobiological Assault Force (XAF): Suggests a highly trained and equipped force dealing with alien or otherworldly monsters.

• The Cryptid Elimination Corps (CEC): A more traditional military-sounding name, focusing on the elimination of cryptids (hidden creatures).

• The Shadow Hunters: Mysterious and evocative, suggesting stealth and precision in monster hunting operations.

• The Grimm Reapers: A darker, more ominous name, suggesting a relentless pursuit and eradication of monstrous threats. "Grimm" hints at fairy tale monsters.

• The Apex Predators: Positions the unit as the ultimate hunters, superior to the monsters they pursue.

• The Terminus Division: Suggests a final, decisive force against the monstrous threat, implying a sense of ending or conclusion.

• The Kaiju Killers: A more direct and action-oriented name, specifically targeting giant monsters (Kaiju).

• The Chronos Hunters: Implies a unit that hunts monsters that may be tied to time travel or temporal anomalies.

• The Void Stalkers: Suggests a unit that operates in dangerous, unknown territories to hunt monsters.

• The Obsidian Guard: A strong, imposing name suggesting a unit that protects against monstrous threats.

• The Aetherial Hunters: Implies a unit that hunts monsters from other dimensions or planes of existence.

• The Necronomicon Squad: A name that draws on Lovecraftian horror, suggesting a unit that deals with particularly ancient and powerful monsters.

These names offer a variety of tones and styles, from the clinical and scientific to the dark and ominous, allowing for flexibility depending on the specific needs of your science fiction setting. Consider the overall tone and style of your story when making your final selection.