Solved! black out the monitor

Solution
It depends on what kind of remote desktop software you're using. If using Windows RDP, remote desktop will display Logon screen, and if proper power settings are in place, monitor will turn off in a while. I don't think you can make remote display complete off immediately.
It depends on what kind of remote desktop software you're using. If using Windows RDP, remote desktop will display Logon screen, and if proper power settings are in place, monitor will turn off in a while. I don't think you can make remote display complete off immediately.
 
Solution
Why you want to black the remote display? You don't what the remote user to see what you're doing, or to know that you're connected?

As I said - RDP will lock remote computer, and (if power settings allow it), the monitor will turn off.