Final answer:
The colonists did not mention King George III's name in the Declaration of Independence because they were not seeking to overthrow the monarchy, but rather expressing their grievances against the British government. The document was a statement of intent to break away from British rule and establish independent states.
Step-by-step explanation:
The reason that King George III's name was not mentioned in the Declaration of Independence is because the colonists were not seeking to overthrow the monarchy or establish a republic. They were expressing their grievances against the king and the British government for violating their rights as English subjects. The Declaration of Independence was a statement of the colonists' intent to break away from British rule and establish their own independent states, not a personal attack on King George III.