The short answer is yes, you can damage your pump.
For a given rotational speed, every centrifugal pump has what's referred to as a Minimum Continuous Stable Flow (MCSF). Flow rates below this will cause cavitation, and if the flow rate stays that low long enough it can result in things like impeller damage, specifically pitting of the impeller face. This happens even if you throttle the discharge.
You can tell when cavitation is happening because it sounds kind of like you're pumping gravel. The bubbles are collapsing against the impeller, making that noise.
Now, the real question is do you need to concern yourself with this? Maybe, maybe not. You probably don't know what the MCSF is for your pump nor do you have a way to measure the flow.
Personally, I wouldn't concern myself with it too much. Just listen to your pump. If it starts to sound like pumping gravel, open the valve a smidge and listen some more.
And yes, you should throttle the discharge. If you throttle the suction you're reducing the NPSHa available to the pump. This also can cause cavitation.