So you want to make sure you have a proper identification, and according to the Deutsche Bahn, your bank card is your best bet. I think the question here is that more what makes your card a debit or credit card.
It depends on how you want it to behave
I have also a bank card that may act as a debit or credit card and have used it extensively either as one or the other, always compatible. On money.SE, the questions I found seem to show that a bank card is not a debit or a credit card, but may act, if the owner decides, as a debit or credit card. Whether this is a debit or credit card determines how the card communicates with the payment system. While this is how you interpreted it for the payment, your question is about the identification. I suppose it is the same, i.e. your card may be identified as a debit or a credit card. My first guess is that if you present your card as a credit card, and the controller uses a machine, the machine will search its credit card features.
DB accepts cards communicating through VISA, MasterCard, American Express, JCB and Diners Club systems
The Deutsche Bahn says it accepts credit cards of the types
VISA, MasterCard, American Express, JCB and Diners Club. So the Deutsche Bahn has systems being able to interact with these types of cards, and in the end what matters is that your card is one of these to interact with the Deutsche Bahn system.
DB identifies your card with first name, last name, credit card number and expiration date
The Deutsche Bahn website says that the identification you show to the controller is what you have stated at the time of purchase. And if you follow the booking flow on bahn.de, the credit card option of identification actually asks you for 4 things :
first name, last name, credit card number and expiration date. I expect that if your card can communicate with the Deutsche Bahn system, what this system will try is matching this information, no more.
This information is written on any bank card (as far as I know). So this means there is no need for a machine to read your card. The controller may just look at the card and read these. In general, I could not find any information apart from this disputed answer that the controller uses a card reader (the dispute is based on the fact that far from all German ID cards could be read by a machine - and no French ID card, though they are an accepted type if identification).
German debit cards use Girocard, yours probably not
On Wikipedia I could find that German debit cards are run on an interbank system called Girocard. This means that the communication protocol for debit cards (how the debit card and payment system communicate) is Girocard, a German system. So non-German cards a priori cannot interact with the German payment systems (they may, if they are Maestro or V-Pay). That's probably why the Deutsche Bahn explicitly writes that
For identification with ec-cards/Maestro, your bank must have its registered office in Germany. So this means that most likely, the controller's machine will not be able to interact with the debit feature of your card, but only the credit feature.
So in the end, while I am no technical expert on the identification of a card, I think that your debit/credit card (as long as it is one of VISA, MasterCard, American Express, JCB and Diners Club) should be accepted as a proof of identification.
An alternative would still be to buy your ticket at any ticket vending machine or at a counter in a station. You would not need any piece of identification. But on some routes, you may pay more buying last-minute at the station than online earlier.