If the money for the unauthorized debit card transaction was taken out of your bank account and not credited back by your bank when you reported it, then yes, you can sue the retailer. You would claim that by failing to verify the identity of the person who was pretending to be you, the retailer was negligent. You would need evidence to support your claim that a reasonably prudent or careful retailer, in the same or similar circumstances, would have definitely asked for identification. If you know someone who has been in a similar retailing business for a few years, then that person could provide this type of "expert testimony." It may depend on other facts, such as the amount of the transaction, the type of retail establishment.