If I have multiple versions of Xcode installed on my Mac mini, and none of those versions have the name "Xcode", what would happen if I upgrade to a newer version of Xcode using App Store? Would it install a new instance of Xcode with the name "Xcode", or would it upgrade one of the other versions?
What do I need to do to install a new instance of Xcode -- the newest version?
The latest version should be the only one named Xcode.
As for having other/renamed versions on your drive, there was a time when the store/installer would sniff them out and nuke them.
If you need to keep an older release version while you download install the latest from the store, move it to a drive you can eject during that process. Also note that preceding Xcode 11 beta, Xcode requires being installed on the boot drive in /Applications.