It appears the WD TV Play Media Player uses DLNA to access network content. There is currently no way to password protect DLNA content due to the DLNA specifications. About the only way to prevent the WD TV Player from playing media from a My Cloud Share is to turn the Media Serving option for the Share off.
One can set a Share to Private and configure User access (Full Access, Read Only, No Access) to the Share’s contents. But that does not apply to the Media Serving option as explained in the previous paragraph.
If you haven’t already done so you may want to read the My Cloud User Manual (http://www.wdc.com/wdproducts/library/?id=439&type=25) which explains how to setup Users, Shares, and the Media Server.
Further the following thread on the Twonky media server within the My Cloud may be relevant.
http://community.wd.com/t/faq-twonky-dlna-media-server-setup-use/95373
