Hi,
The information you were given about having a year of warranty for your Surface Accessory is correct. The warranty for accessories is provided upon purchasing the product. You wouldn't need to register it. All you need to present when taking the device for service or replacement are the records that you were given when you bought the accessory.
You can also speak with the Microsoft Store Sales and Customer Support teams if you have other questions. Go here for more information.
Regards.