Can't change SSD's icon

The system is on a locked container that is read only. That's why you can't change the icon of that container/partition. It's all part of Apple's SIP, System Integrity Protection. I have a bootable external SSD and only the Data container mounts on the Desktop. The system portion never mounts.

I made my clone with Carbon Copy Cloner and was able to change the icon on the one container that appears on the Desktop - which I assumed was the Data container as it holds all of my user data. However, in Disk Utility both show as mounted but only one shows just like the internal boot SSD:

Internal Boot Drive

Cloned External Boot Drive

This is what Disk Utility shows about the two:

The internal boot drive shows a snapshot as being mounted but it's not seen on the Desktop. Don't know why it shows up and doesn't affect performance or storage capacity in any manner. "Tis a puzzlement".

By what process did you arrive at the “bootable backup?”

I’ve seen a few reports that they cannot rename a cloned start up volume. This may be the same issue where that clone drive is locked to changes like that.

Normally, you should be able to change the icon and rename the drive in the Finder. The custom icon is actually written to the data volume not the actual start up volume which has noted is mounted read only.

Do you mean the startup Data volume, or your redundant data partition you made?

The OS is already divided into System and Data. The OS Data volume should not mount on the desktop and is where the custom icon is actually stored.

Interestingly, however, in the Startup Disk settings window as well as Disk Utility the custom icon does show.

It is probably some artifact of the cloning process. A normal startup volume will show the custom icon on the Desktop and everywhere else. Because of the clone, the system may not be able to link it to the Data volume.

Are you started up from that back up drive? You won’t see the icon in the main drive if it’s not the start up drive because the icon is actually stored in the data volume. if you’re not started up from that there is no linkage between its data volume and the main system volume.

In my last reply's screenshots I was booted into Toad Hall and the cloned TH - Ventura also showed the custom icon. I have two other bootable external SSDs, High Sierra and Mojave, both with custom icons and they both show when mounted and not booted into. Or did I misinterpret your last reply?

You can assign a custom icon to an unmounted system volume and that will stick with it regardless of being booted. If you add a custom icon to booted system volume, it goes into the associated Data Volume. That doesn’t link back the an unmounted System Volume. But, I have not tried on Ventura. Maybe Finder makes the association, now.