As this is one of the top results for Windows not showing an HDMI audio device with a comment section, I hope I can provide a fix for a very stupid reason I had trouble for over a year. If you make the same stupid mistake of having left an HDMI cable going from the receiver to the monitor, Windows CAN recognize the device with enough driver reinstalls and restarts, but it is extremely confused. My specific issue was I had video going directly from my GPU to the monitor via DisplayPort, and an HDMI cable to the receiver for sound, but I had left an HDMI cable going from the receiver to the monitor. Windows was confused because it was seeing the same device in multiple ways it could not make sense of, and as soon as I fixed this dumb mistake, Windows no longer randomly wouldn’t see the receiver if I restarted or changed the source on the receiver. Now I can actually use my other sources again and Windows immediately moves over to the computer audio when I turn it back.