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Add possibility of rename Backup folders. If you have only one computer, it go fine, but if you have more than one, it ends being very confussing. Due iCloud Drive issues, I've changed all of my Macs...
Even if it turns out to be impossible to allow renaming for technical reasons, perhaps you could allow us to give "nicknames" to each backup, shown alongside the main "Mac (x)" name? That would solve most of the frustration, without needing to resolve name collisions etc, which I assume is the holdup on your side. What I mean is, if a user gives two computers the same nickname, that is their fault, and it is reversible by them, since you are still using your "Mac (x)" as the main name.