I would think WD goes by the serial number and some drives have the date on the label too. If that info does not satisfy them, they think you’re lying about the purchase date, they’ll more than likely ask for proof of purchase.
"The term of your limited warranty period shall commence on the purchase date appearing on your purchase receipt from an authorized distributor or authorized reseller and extends only for the period of time set forth in the Product documentation.
Proof of purchase shall be required to be eligible for this warranty and to establish the commencement date of this warranty. To verify the warranty of your Product and update your purchase date (if required), please use our online Warranty Status Check service. In the United States, some states do not allow limitations on how long implied warranties last, so the above limitation may not apply to you."