Officially you cannot restrict access to the default Public Share folder nor can it be officially set to Private like other Shares. This has been a common complaint for years. What you can do is turn off Media Serving on the Public Share to prevent DLNA clients from being able to access media content in that Share. One could put thier media in Shares OTHER than the Public Share then restrict access to those Shares by setting them to Private and limiting who has either Full Access or Read Access to the Private Share. Because of the way DLNA works it can still access a Share even though its set to Private provided the Media Serving option is enabled for that Private Share.
Unofficially there are way to try and deal with this issue, but it involves modifying one or more firmware files using SSH.
See the following links for more information:
https://community.wd.com/t/manage-public-share-user-access-at-least-a-read-only-option/97231
https://community.wd.com/t/public-share-public-access-on/96854
https://community.wd.com/t/removing-public-share-wd-mycloud/137086
https://community.wd.com/t/faq-twonky-dlna-media-server-setup-use/95373
