The problem of renaming the macOS boot volumes is due to how macOS 10.15+ deals with the new read-only system volume and how Apple has macOS trying to make them appear as a single traditional volume to the user within the Finder. Unfortunately each version of macOS 10.15, 11.x, and 12.x uses different behind the scenes "magic" to make this appear seemless to the user. Unfortunately macOS 12.x (and perhaps even 11.x) make this even more difficult by hiding the behind the scenes "magic" and links even from the command line utilities which usually reveal everything. With macOS 10.15 Catalina Apple it was possible to modify the base name of one of the "boot" volumes and it would automatically change the base name of the other "linked" volume, but unfortunately Apple seems to have removed this ability with later versions of macOS (I think even a later patch to Catalina as well). Unfortunately renaming the "drive" name from the Finder does not automatically change the base name for the other linked volume (or if later versions of macOS can do this, then it may be break at times).
Now to the other part of the problem which still needs to be solved. Since the latest screenshots from Disk Utility show all your system/data volumes are now correctly named as a set, it must mean the drive label which is used by the Apple boot picker menu was not modified when you modified the boot volume name(s). The drive label is actually a specially formatted image file that is hidden somewhere on a macOS boot volume.
On older versions of macOS this would have been a simpler fix due to the single volume used by older versions of macOS. Also, the command line utility used to do this has been deprecated by Apple for years so I have no idea if it would even with any macOS 10.15+ boot volumes. Plus I've never had to change the label of a macOS boot volume before so I'm not certain how to do it with the command anyway. Experimenting may be dangerous and could potentially make that OS volume (or another one) unbootable.
I have created custom boot labels for external volumes for non-macOS boot volumes since I understood how the non-macOS boot volumes worked and could risk the dangers of experimentation. Unfortunately there is very little information about how to make this change to a macOS boot volume (especially with macOS 10.15+). I did locate one thread on a non-Apple forum which included a command (along with a few others to change other options), but I hesitate to include the command here since I don't know what will happen to the OS if it is used incorrectly and I'm not certain the suggested command was even successful for the user. Plus it also requires the user to understand the command line in order to be able confirm the exact mount point required since you have multiple volumes on your drive which complicates things.
A better and easier option would be for you to use the rEFInd boot manager (may be an Intel only option -- I don't know if it has been updated to work with M1 Macs). rEFInd allows you to custom the item names which appear within the rEFInd boot manager for the various boot volumes on your Mac.