The lack of identifying numbers causes no end of confusion when I travel with it too, especially in European countries that Apple haven't launched the card in yet.
It got so annoying on a recent trip, I just reverted to using another conventional credit card. The Apple Card is generally fine any time I use tap to pay from the phone, but the physical card simply isn't as reliable as some other cards I have that generally "always work" abroad. I've even had restaurant staff treat me very suspiciously over the blank card.
Its also an odd card in that the physical card itself has no tap-to-pay functions at all; of course Apple want you to use the iPhone it can't operate without to do this part instead. Again though, if I do have to hand over the card, in Europe people will of course try and tap it instead of a swipe and once again confusion reigns.
Oh and if a server drops the card, it makes the most irritatingly loud clang being a small metal object - I would happily go back to plastic for the card!
I went to Europe and used Apple Card almost exclusively with zero issues. Both via Apple Pay on my iPhone as well as using the physical card. Seamless experience.
I have an Apple Card. The only text on the card is my name. I think a lot of bank cards are starting to do similar stuff.
It isn't foolproof, though. Someone somehow was able to charge against the card, a couple of months ago.