You should report this to law enforcement as a possible case of identity theft. You should also contact the company that wrote the letter to get all information they have about the application and the person who applied, as this may be helpful to police investigating your case.
Finally, it is probably also a good idea go to www.annualcreditreport.com to get free copies of your credit reports from the three credit bureaus. This will allow you to see if there are other unknown debts in your name. If there are unknown debts, you need to use each credit bureau's dispute process to try to get them removed from your credit reports.
(The attorney responding is licensed only in the state of North Carolina. This response does NOT constitute legal advice and does NOT create an attorney/ client relationship! Rather, the response is in the form of legal education and is intended to provide general information about the matter in question. Although a response is provided to the specific question, there may be other facts and law relevant to the issue that the questioner has left out and which would make the reply unsuitable. Therefore, the questioner should not base any decision on the answer, but should confer with an attorney in person about the specifics of his or her case.)