Unfortunately, there is no large database of auto insurance providers in United States. Because of this, you will not be able to look up which car is insured and who the insurance company is. However, there are other ways that with some extra effort you could figure out who the auto insurance provider is.
If you have the driver's contact information, you can reach out to them directly and ask them.
As a second step, you should Google each of the names that are listed. If they are insurance agents, they should have a website or online profile that can help provide you with contact information.
Another way to figure out who the auto insurance provider is would be to contact the major insurance agencies. There are about five major insurance companies in the United States that provide the majority of insurance. While they are not necessarily obligated to do so, they may be willing to confirm whether or not they provide auto insurance to a certain individual. Having an individual's name and type of car should be enough to confirm whether or not they have insurance with each individual insurance company.
If that doesn't work, the next step would be to take the driver of the other car to small claims court. By filing either a criminal or civil suit, you will ultimately be forcing the person's hand to acknowledge who their auto insurance provider is.while this may sound like a stressful and time-consuming process, your auto insurance provider will probably be able to assist you with part of the process.