Site name in Windows Explorer

Bas_B  Are you referring to the way your document libraries look in file explorer after you've synced, like this?

I get an error when I try to rename that "folder" (that's what you'd have to do to hide the site name). I'd argue this isn't a big deal--if you're syncing document libraries from multiple sites, you quickly enter a scenario where you might have document libraries with the same name in different sites, and you certainly do at least for the out of the box Documents document library. Microsoft would have a serious user-experience problem on its hands if it defaulted to carrying over just the document library name instead of both.

I don't have an answer as to why Microsoft doesn't let you rename locally. I can make a wild, unfounded guess--it might be that, while syncing libraries carries over all the rights you have against the document library, Microsoft has deemed that renaming the folder--which is at least the same as renaming the document library itself--isn't something that the sync functionality should allow someone to do.