This is not to scare you however you should do a credit check through Equifax or one of the other credit bureau forums. This will let you know if any one has applied for anything else.
About 12 years ago something similar happened to my son. He got a bill in the mail from one of the mobile phone companies, I can't remember which one, and the bill was sent to our address. As he was not living here at the time I called him and asked if he wanted me to drop it off. Turns out he never had a phone with this company. It was purchased in his name, using his credit and information, our address. He contacted the phone company and put a stop on it but it took tons of paper work. That was just the beginning. This person, or persons, took out a loan at one of the credit unions near where we live, got a check for the loan and went to a payday loan store to cash it. Then they went to Future shop in Scarborough and bought a ton of stuff. A few other things happened as well. When all was said and done the total of the fraud exceeded $25,000. The one saving grace to it all was that the credit union actually kept copies of all this persons information. He had made up a pay stub from the company my son actually worked at. He had a sin card in his name and a drivers licence. The person was African American. My son is not. That help clear up the companies who did not want to believe it was not him.
My son put a alert on his credit bureaus, any time there was a hit he was to be notified. There has been no issues since.
My point is to be aware, head it off as soon as you can and by contacting the CB you may help prevent any further issues. They will know if anyone has applied for any other credit in his name, or yours for that matter.