By choosing PREMIUM plan you'll have an option to make your screen private. If you do this, others can't advertise on your screen, and your screen won't show up in screens search. You can choose this on your screen's edit page under Advanced settings.
You may also keep your PREMIUM screen public, in which case others can buy advertisements to your screen. To choose this make sure "private screen" option in Advanced settings is not checked.
Note, that your screen goes public automatically, when your paid PREMIUM time ends. To keep it private your can pay the next month in advance in Shopping cart
. If PREMIUM ends and you start it again, you may set the screen back to private.