I do not know the answer, but noticed that for polygons, the CenterAtOrigin script does not place the center of the polygon at the origin.
It does place the center of the bounding box of the polygon at the origin.

Hi nos,

> Is there a way to click on a centerpoint and the corresponding object gets selected?

Sorry, no there is not currently any way to do that - those center points you are showing there are object snap points, they're used as snapping targets and object selection is basically a different task than that.

I guess you could hide your objects and then show them one by one and check out the center of each currently visible one, by hiding others that would let you identify which object's center point you are currently viewing.

- Michael