Have people repeatedly asked for a search feature for the remote apps? Yes, see the many Cloud Ideas links at the end of this post.
Can you search for files remotely? Actually yes. One can use the WebDAVMod that would allow one to remotely map their My Cloud in Windows File Explorer and from there one should be able to perform a search (which might be slow) for files on the My Cloud. One can even use a file manager app like ES File Explorer on their mobile device (Android) and remote map their My Cloud using the WebDAVMod and search for files from their Android device.
http://community.wd.com/t/app-clouddavmod-v1-0-for-firmware-v4-05-2016/161543
Or can setup some sort of VPN or even Remote Desktop connection to your local network and access the My Cloud that way using Windows File Explorer.
One can add their opinion to one of the following threads in the Cloud Ideas subforum and hope that WD eventually gets around to adding a search option to the remote apps/programs…
http://community.wd.com/t/wd-my-cloud-needs-search-bar/97252
http://community.wd.com/t/search-functionality-in-mycloud-desktop/151973
http://community.wd.com/t/search-funktion-in-my-cloud-app/96944
http://community.wd.com/t/search-indexing/160783
http://community.wd.com/t/search-feature-in-mycloud-desktop-app/97126
Or any of the many other threads in the Cloud Ideas subforum asking for the search feature.