Yes, CCC will display both volumes. APFS is an option in Mojave but not in Catalina. The Data volume shows up in Mojave because Mojave does not keep the Data volume invisible as it does in Catalina. This was due to the fact that Mojave was not fully converted for APFS.
Open Disk Utility which will display both volumes in one container. Select the volume whose name should appear in the Disk Utility window at the top. Double-click on the name in order to make the change. If you change the name of the startup volume, then the Data volume's name should change also. This is in Catalina. I haven't tried it in Mojave.
There is always a problem with File Sharing where all users may have the same volume names. However odd that may appear on screen, the OS knows which is which ......, usually. For only one additional volume, a different icon is used for the shared volume when it is mounted. This would distinguish it from the server volume.