I am entering this post on my late 2012 Mac Mini. Inside it is a Samsung 840 Pro 256 gig SSD, and I have only one partition on it entitled "Macintosh SD". It is the boot partition.
I have an external enclosure attached (via USB) to the MIni, and within that enclosure is a Samsung 850 Pro 512 gig SSD. I have 3 partitions on it:
Mac Mini Backup SSD
MacBook Air Backup SSD
Other Files SSD
Those first 2 partitions (as their names imply) are SuperDuper! backups for each of my Macs. The third one contains various files, folders, etc.
After booting up my MIni from its internal boot drive, here is the order of those "devices" on my desktop, on the right, starting from the top:
Macintosh SD (grey colored disk icon)
Mac Mini Backup SSD (orange colored disk icon)
MacBook Air Backup SSD (orange colored disk icon)
Other Files SSD (orange colored disk icon)
When I restart the Min i from the Mac Mini Backup SSD partition (again, made with SuperDuper!), the order of those "devices" on the desktop, on the right, again from the top, is:
Mac Mini Backup SSD (orange colored disk icon)
Macintosh SD (grey colored disk icon)
MacBook Air Backup SSD (orange colored disk icon)
Other Files SSD (orange colored disk icon)
Similar "arrangements" occur also for my MacBook Air, and also for the other external Samsung 850 Pro 512 gig SSD that I have.
Here is one thing you can try: rename one of those external partitions (you can do that by clicking on the device name under the icon). It would be best if you give it some "unique" name that is different than the one for your internal boot drive).
Finally, I have never needed to change any kind of "setting" for that order I mentioned above. That device order appears no matter what Mac OS I have used. In fact, I don't even know how to change it.