> I have no way to add an alias or distinguish them otherwise.

Seeing ones own name on a physical card also doesn't say say which joint account it is, yours or your partners (my partner and I each have Bank X, and each have a card for the other, which only has our own name, so, I feel your pain).

But, there is a way!

1. Tap the card, then tap the card[123] icon upper right and "Enter physical card information".

2. Either scan the card or type it in. Add the CVV while you're at it, seeing this later requires an additional FaceID.

3. Add "Description" for "Mine" or "Joint" or whatever. (KEY STEP)

When asked if you want to replace the card with same number say yes. It'll stay the same card, same transaction histories, etc., but now have a distinguishing description.