First time dedicated GPU.

[MiRai]

I've confirmed that the issue with the game client and same-name GPUs still occurs, and so you'd need to...

1) In the Device Manager, look at the Details tab of the GPU to get its Driver Key
2) Go into the registry and search for that value (it should lead you to HKLM\SYSTEM\ControlSet001\Enum\PCI\{Device Instance Path} on W10)
3) Adjust the DeviceDesc of the GPU and give it a unique designator so that it has a unique name (e.g. add a "1" or "2" at end of whatever is stored in that key)
4) Repeat steps 1-3 for each GPU you have

After finishing all of that, you will need to restart your computer before those changes are picked up by the game client, and, as always, messing around with the registry can screw things up, so good luck. I'll be doing this again later today so that I can submit a bug report to Blizzard, so maybe I'll have a more detailed guide today or tomorrow.

Additional Information:

1) You will need to have a proper Window Layout (you already know this)
2) You will have to adjust which monitor is assigned in the video settings for any game client not assigned to the Primary display (numbers may be wrong in the WoW client, so try all available options while monitoring hardware - Monitor 1 and Monitor 2 were reversed for me)
3) You can leave the in-game GPU assignment set to Auto Detect and WoW will assign it to the proper GPU as long as the Monitor drop-down is properly assigned
4) Changes to either the Monitor or GPU drop-downs require a complete restart of the game client to take effect
5) This does not work for DX12, only DX11

EDIT1: Honestly, now that I'm trying to do a guide for this I can't replicate the issue. -__-
EDIT2: Yep, no idea. I even did a clean reinstall of the driver to wipe everything thinking that I screwed something up trying to manually revert the changes I made, but no dice—I cannot replicate the issue, and I am having no problem splitting the load between two GPUs on two different displays in DX11.