First of all, you lent your card to someone else.
Secondly, it doesn't matter whose name he signs! Because the law does not stipulate that you can't have the same name! Just like if your name is Zhang San and your friend has the same name as you, he will take your card and sign Zhang San. Do you think he signed it under your disguise? Or did he sign it? In fact, the signature is not important, especially some businesses, in order not to get into trouble, will ask the other party to sign the name of the credit card. After all, your name is spelled under the card, so it's easy to see whose name you signed.
If you lend your credit card to others, once there is a problem, then the card is yours and you must bear the corresponding responsibility!
Unless you completely abandon friends and other relationships, you can report it, and you can report financial theft!