First of all, request a copy of the ID and credit card from your customer in order to verify that the name on the card matches the name on the ID. If you question the legitimacy of the payment, do not ship the items and freeze the order. After the transaction is proved to be fraudulent, immediately refund the charge to the cardholder; otherwise, the legitimate cardholder may demand for a chargeback. Make sure the 3D Secure feature is activated and works properly in order to prevent the further fraudulent activity.
Here you can find additional resources that may help you in the process and tell you more about payment processing.
If you haven't found answers to your questions here or need any further assistance, don't hesitate to contact us.