No, not really. You cannot set the main Public Share to Private either. Its a complaint we’ve long been making.
There are however unofficial methods of possibly hiding or removing the main Public Share. Here are two discussions on hiding the Public Share. Use the forum search (magnifying glass icon upper right) to find other discussions on this issue.
https://community.wd.com/t/can-i-delete-or-rename-public-folder/91213
https://community.wd.com/t/hiding-or-removing-public-share/91932
