Thought for the wonderful The Godzilla Papers:

Monarch: Legacy of Monsters focuses more on the human characters of the show instead of the Kaiju, specificaly the descendants of Monarch’s founders, often creating drama around the characters’ dark sides.

A legacy is something that will outlast you.

The Kaiju are seemingly eternal, and therefore have no legacy.

The name doesn't refer to the Kaiju, it refers to the humans. The humans are the monsters who destroy each other to rule the planet while the Kaiju just follow their instincts.

The humans are the monsters in the show (specifically Apex Cybernetics), while the Kaiju are simply caught in the crossfire.