Hello! 

Thanks for contributing. From the Bing StreetSide, you're totally right that the shared driveway here erroneously has a name tag on it. I've updated it to be a marked as a shared driveway.

As for access, "private" in this context means that it is posted that no one can use it. The more common tag for access on driveways is "destination" or "permissive". You can read about the distinctions here. https://wiki.openstreetmap.org/wiki/Key:access. In general, software treats driveways with lower priority so almost all the driveways have no access tag.

Happy mapping!