Thanks for your suggestion. Due to the static nature of one Presentation appearing on multiple displays at the same time, there isn't a way to display the ID or Display Name on the actual unit when testing. I will however suggest this to our team for future development, perhaps in a "Special Flags" area of the software. In the interim, I would recommend giving the Displays you have on your Account unique names which are descriptive so you can identify them.
Also, I have found just making a label and sticking it to the NUC or the rear of the hardware display/monitor is useful in identifying displays. Another option is to use the MAC address of each of your NUCs or computers running the Player, and on your network, just making a note that XX:XX:XX:XX:XX:XX is "NUC in Lobby" for easy reference.