Can your employer force you to put the company name on your auto insurance if you drive your personal vehicle to do company business?

If the employer is compensating you for the use of your truck, i.e, a mileage rate, then yes they can ask to be listed as an additional insured. However, if they fail to pay you anything for the use of your vehicle, they have no right to demand anything regarding your vehicle. It should also be noted that if you have an accident while in the performance of your employment, they are ultimately liable. Make sure you inform your carrier that you are using the truck for their work - then watch your rates go through the roof.