Unfortunately for the single bay/single drive My Clouds WD decided that users cannot set the main Public Share to Private through the Dashboard, meaning there will always be one Public Share that anyone can access on the My Cloud if one can gain access to the My Cloud.
Currently one would have to use SSH to modify the firmware files to disable the Public Share or change its settings. Its something that has been complained about several times in the past.
https://community.wd.com/t/public-share-public-access-on/96854
https://community.wd.com/t/removing-public-share-wd-mycloud/137086
The Cloud Ideas request (so far unheeded by WD):
https://community.wd.com/t/manage-public-share-user-access-at-least-a-read-only-option/97231