To sue in a state court, one needs to have a "cause of action." There are numerous causes of action, such as "breach of contract," "negligence," "fraud," "unjust enrichment," etc., as well as causes of action rooted in statutory law. Every state has their own although they are very similar to each other in every state because they all stem from the same common law. A pleading in Court needs at least one cause of action, although it is not unusual to have more than one.
Someone in your situation can threaten to sue for defamation. The elements of defamation are: the statement caused reputation loss to the you, the material in question referenced you, they are responsible for publishing or speaking the statement under review, the statement caused harm, and there was damage caused.
A letter threatening to sue them unless they pay damages may do the trick. However if they do not budge, then one may have to actually file a lawsuit to get this taken care of. Let me know if you need a sample letter.
I hope this helps and clarifies. Please use the SEND or REPLY button to keep chatting, or please RATE when finished. You may always ask follow ups at no charge after rating. Kindly rate my answer as one of TOP THREE FACES/STARS and then SUBMIT, as this is how experts get credit for our time. Rating my answer the bottom two faces/stars (or failing to submit the rating) does not give me credit and reflects poorly on me, even if my answer is correct. I work very hard to formulate an informative and honest answer for you; please reciprocate my good faith with a positive rating.