Stores would offer sales coupons to regular customers. This was till a few years back.
They then started issuing credit cards linked to the store's brand. Use of this card gave you credit points which could be redeemed later. This has now moved on to normal credit cards. These regular cards have tied up with stores and brands and offer redeeming of points for goods and services offered by these brands.
Off recently I have noticed that more often than not the billing clerk asks for your mobile telephone number. Your phone number has become your identification number. Your name appears magically the moment your phone number is typed in the billing clerks computer.
Two people can have the same name.
They are unlikely to have the same mobile number.
In so many stores now, our phone is our identity. (also see my blog post 'The ever changing telephone')