You are not liable for them unless you guaranteed the debts, or signed for them, or at least directed or caused them to be incurred or taken out. That said, it is far from unlikely that a creditor will, if the business is in your name, sue in the belief they are your debts or that you incurred them, etc., forcing you to show that despite the business name and relationship to your father, you are not involved. Send your father a letter, sent some way you can prove delivery, instructing him to cease and desist from using your name with 15 business days, on the ground that he is 1) effectively defaming you, by causing you to be connected to unpaid debts; and 2) is using your name for his economic advantage without your consent. If he does not stop, then file a lawsuit for defamation and for unauthorized use of your name and/or likeness; seek a court order forcing him to disassociate you fully. This will also help stand as proof that you are not connected to and did not authorize what is going on.