How to sue an insurance company?
An insurance company just like everyone else has to defend lawsuits. When you sue someone, you get in a car crash and then you're suing John Smith, but really you're suing him but he is being represented by his insurance company. The defense is paid for by the insurance company. The insurance company is the one providing for payment for compensation.
Also, you may have a situation where you have uninsured motorist coverage in an automobile accident where somebody hits you, they don't have insurance, so you have your own insurance, you would file a direct action against your insurance company. Almost every lawsuit and you see it in court, you're in front of the jury or if you're a jury you see that they have representation or counsel but really it's the insurance company that's running the show whether that be litigation and the defense for them.
The easy thing to say is you can sue an insurance company by filing a lawsuit. While they may not be the direct named party, they are the one behind the scenes kind of running everything where they are paying for the defense and ultimately for the compensation.