What can you do if you report to a credit card company that your husband took a credit card out in your name and you reported it to them and they did nothing?

If you are married, your husband can definitely apply for a credit card in your name. This is commonly done. Some husbands make their wives as supplement to their credit cards or apply for a separate card. So, the credit card company may not find anything wrong with what your husband did. Not unless, you and your husband are having problems, then if you have a case, better report it first to the proper authority before you approach the credit card company with your complaint or case.