Markers Showing Header When Hovering (storyline)

Unfortunately, there's no way to turn off the hover for a marker. 

You could create your own markers, with the content added in a Selected state. When an object has a Normal state and a Selected state, it will automatically toggle between those states when the user clicks it, so you wouldn't need any triggers to change the state.

You would have to put all of your custom markers into a button set to ensure that selecting one would deselect the others. And, of course, you'd lose the built-in functions, like being able to quickly adjust the direction or size of the label. But they wouldn't show anything when hovered (unless you added a Hover state).