Is there a way to hide HDDs on the Desktop?

[lostPod]

Please see attachment picture. Is better than words.

What is the application with the eyeballs on the menu?

 

[I WAS the one]

What is the application with the eyeballs on the menu?

Eye Balls App

 

[Daniva]

sudo SetFile -a V /Volumes/"Drivename" killall Finder

where Drivename is (obviously) the mounted name of the drive to be hidden. Replace the uppercase V with a lowercase v to make the drive visible again.

Thank you @Grumpus, that's the best and correct way to hide a volume of an APFS disk.
The volume disappears from the desktop but it's still mounted and visible in Disk Utility. In the case of a Time Machine we can see that the volume is still mounted by doing a backup with the volume hidden 👍

 

[jdw13]

As mentioned before, it appears to me that OnyX does exactly what you want, under Files/Visibility/Volume