As far as I know, AMD doesn't require you to register an AMD product at their website.
All AMD PIB (Processor in a box) have a three year AMD Warranty. All you will need is proof of purchase indicating Date of Purchase, that you are the original purchaser, amount paid, and Invoice or Billing number. As long as AMD doesn't consider your Warranty request as "Customer Error" it should be covered under AMD Warranty for 3 years at the Date of Purchase.
I believe that you must first go through your Retailer Warranty first before AMD Warranty becomes effective. Not sure though.
AMD can verify that you have a legal AMD processor by the Serial Number and Model Number that is printed on the processor or from the original AMD Box.
Here is AMD Warranty Request : https://www.amd.com/en/support/kb/warranty-information/rma-form
Here is AMD PIB Warranty which you can read yourself: https://www.amd.com/en/support/kb/warranty-information/rma-03