It would be great to have an option which enables end-users to manually define the synced folder name per document library. (similar like Shortcuts to websites)

The reason is that, renamed SPO site titles are not replicated to the synced folder names, which confuses some users when they are talking about the same "sites"/"team" but with different names.
If end-users are aware, that they have defined the Name for that folder themselves they know that the corresponding site must not correlate to their own name.