Not necessarily an id theft
It’s more likely a credit report error. It’s very unlikely for an identity thieve to use someone else’s identity for a mortgage, because it can be easily traced back to him.
Identity thieve almost always apply for personal loans and credit cards, max them out and then default on them.
It’s more likely that it’s a clerical error by the credit card company, the mortgage company or the credit bureau. Dose the mortgage appear on your credit report from all the 3 major credit bureaus or just on one?
If the account appear on just one credit report, it’s probably a credit bureau error that can be sorted out by a simple dispute.
If it appears on your report from all the 3 major credit bureaus, it can be a clerical error made by the mortgage company or by the credit card company you applied to. You can find the mortgage company details in the “Contact Information” section of your credit report. Start investigating with them.
If you do have reason to believe that this is indeed an identity theft, follow the steps in this ID Theft Guide for more help with ID theft.