I also had this requirement and I analyzed it, and according to me, the system does not have this functionality, except as you say, perhaps by modifying the template, but the truth is I could not tell you how, I did not try.
If you analyze it, the requirement does not make sense, but I understand that the operation of a restaurant is capricious.
First of all, the RVC is where the purchase was made, where the income goes. On the other hand, the function of the KDS is to indicate what to prepare, how to prepare it and where to deliver or serve it (Dining Room, To-Go, Delivery, etc), that is why the KDS shows the Order Type and not the RVC.