Now, Luna also has an ID card.
However, at the moment it seems that other than being used to register as a member of the travel agency and set up online accounts, her ID card doesn't have much use—after all, the appearance of this Artificial Saintess is too conspicuous, making it even harder for her to go out than Erin. At least Erin can be held in Hu Li's arms or packed in a tote bag, but for Luna, who's over two meters tall, going out means she'd have to be wrapped up tightly like cosplaying as an Astartes...
Of course, Luna herself actually has no interest in going out; her biggest interest is finding a spot at home where she won't be in the way, and just standing there until she freezes, only to reboot temporarily when someone comes around.