They can file a lawsuit against you/your business because the courts do not pre-screen lawsuits to make sure they are good or valid before accepting them. But if you can prove that this wasn't you (and/or the people suing you cannot prove that it was, since the burden of proof will be on them to establish their case, as the persons suing), you should be able to defend against any such suits successfully. You would only be responsible if you participated in the fraud: you are not responsible for anything you did not do or participate in, even if done (without your consent) in your name.You should file a police report against your brother for doing this--not only is that legally appropriate and fair, since fraud and stealing your business's identity are in fact crimes, but it will help provide evidence that you did not in any way collaborate with your brother in doing this, or authorize/sanction his scam. You can and should also sue your brother for any costs or losses you incur due to his actions.