I don't know that there is a what to make it completely hidden, but if you add security to the folders you can make it so login is required to see the the services. Security and blocking access can create other hoops to jump through, especially if you do not want all users to be prompted, and depending on where you and what applications you are using to access the data.
Additional details of your desired workflow would probably be necessary for any other advice. You may want to take a look at this doc:
Server Implementation Guidance—Trust ArcGIS | ArcGIS
Just as a comment, we have some folders that are public, others that require login credentials. For web activity, we use proxies and tokens so users are not prompted for login. Internally, staff still needs to log in to see secure folders/services thru the Services Directory. I'm hoping to eliminate the staff login myself, but not working on that right now. Also, depending on wheat version and patches you have installed, the behavior for access to secure Services Directory differed slightly (i think 10.4.1, maybe with a patch, required you to know the exact folder, and log in there...vs on login for all the secure folders you had permissions to. We are still using 10.2.2, but plan to upgrade to 10.5.x).
