I suggest taking it a step further as I have. Go to the websites of each of the three credit agencies and place a credit freeze on your identity. It costs $5.00 each (when I did it years ago), but makes it impossible for somebody to open a new account in your name. As a bonus, all the credit card offers that stuff your mailbox every day will stop almost completely.
Thieves sometimes steal credit card offers out of your mailbox, apply and then check your mailbox for the new card when it comes. They then immediately change the account address. By the time you realize what has happened, the thief could have run up thousands of dollars in debt.
Does that change your credit rating?
Good advice, thanks.