How do I add a label to identical cards in Wallet?
This doesn't appear to be possible at present. (See Apple discussions 8208759 and 8126880.)

As you point out, the only currently available options seem to be sorting your cards in an order you can remember or relying on details like a card balance or the last four digits of a card number.

On the other hand, if it's important enough to warrant the trouble (not to mention the awkwardness), you could perhaps create your own dummy cards and use them as labels, naming each for a card you want to identify and sorting it above the card it refers to.

You can request a feature at https://www.apple.com/feedback/iphone.html.