While some vendors may have operated that way, that’s not what a 2 year warranty means. The warranty doesn’t guarantee that the device will last for two years–it guarantees that the purchaser won’t pay a second time for the product (or service) during the 2 years. The two years starts at the time of initial purchase, and ends 2 years later regardless of whether or not product replacement has been made under warranty in the meantime.
Usually it’s written as the original purchaser and the original vehicle.