Deutsche Bahn requires travellers with online tickets to select some form of identification. For non-Europeans, the only practical option seems to be a credit card, and the website asks for the name and card number. Is a MasterCard debit card without the cardholder's name printed on the card acceptable?
As far as I understand, the DB is not concerned about ID at all. A credit card has no photo and the conductor does not need to ask for another ID to match you to your credit card. The whole point is to avoid any reliance on photographs or identification of the person carrying the ticket. The process should therefore be quicker and could even be fully automatized.
The logic seems to be that the card whose number you entered when booking is a token that is unique in the whole world, thus precluding anyone else than the card holder from using the same ticket at the same time. In fact, bahn.de stresses that you should take the exact card used to book the ticket, even if it's not valid anymore. Therefore, it shouldn't matter if your name is on it or not.
At the same time, I have no actual evidence for this and did not try it myself. In practice, I don't think they usually match the numbers and I can easily imagine they would be surprised.
I came across a forum post from someone who had no problem using a ticket on which he entered the wrong number (which implies that the conductors did not scan/check the numbers but only looked at the name) but almost got fined for it later in the trip.
I wrote an email to DB asking about this, and they responded,