Under the terms of the Warsaw and Montreal conventions, all luggage should be identifiable to the passenger, in writing not merely by description.

So, YES, sort of. The tag does not have to be external. I use a business card with my home address written on the back, in an inside pocket.

Many Airlines like to issue paper elasticated tags so they know it is done, and in the hope you will be displaying their logo for a few days afterwards. And it is their responsibility to check the protocol is complied with. Ryanair and easyjet do that for self-checkin by burying it in small print. Most carriers blithely don't bother at all. We are all seasoned travellers and know the rules.

And that is why some airport shops, in the few countries that support the rules fully, staple a receipt to the bags of duty-free.