Can my license be suspended if I collected car insurance money from two different insurance companies from an accident?

If you don't pay for the damage caused if you were uninsured, you can be reported to the DMV which can suspend.

If the company sues you, and you fail to pay a judgment, they can suspend your license. Otherwise, they cannot just suspend your license.

In Georgia your license will be suspended if you do not have car insurance. How the police or state will find out if you do not have insurance depends on the situation. Will Geico report you? I cannot answer that. However, your question heading is totally different then the scenario, so I am confused on what exactly your concern is. For the two accident situation, there are scenarios where you can collect from multiple car insurance companies depending on who is at fault, the amount of damages, and the amount of liability insurance.