This can be a tough situation and often in these fringe cases, it can very difficult to determine with confidence if an order is legitimate or not. Asking the customer to provide a form of identification and the last four digits of the credit card is an appropriate measure to take the fact that the customer provided this immediately is a good indicator that their order is genuine, but it still cannot guarantee it. In many cases where a chargeback is issued, the order is legitimate but the customer may choose to issue a chargeback in future with no clear reason why.
I would recommend checking out the documentation we have on fraud prevention and preventing chargebacks for further guidance, but ultimately as the responsibility of handling any potential chargeback lies with the merchant, the decision on whether to accept the payment and fulfill the order is down to the merchant as well. Shopify does offer some fraud prevention features you can consider, such as the Fraud Filter app and Fraud Protect, the latter of which is available if you use Shopify Payments as your primary gateway.
While this answer may be unsatisfactory, Shopify cannot advise with confidence whether or not you should fulfill a suspicious order or if you would be likely to win any potential chargeback, and ultimately you should use your best judgement on whether or not to fulfill the order with the help of the tools we provide.
Victor | Social Care @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog