Hey iStark,
We have not heard of any plans to add the monitor selection to the options in Heroes of the Storm. Heroes of the Storm should always launch on your Primary monitor, determined by your Windows display settings.
If you have Windows 10 or Windows 11 there may be an easier way you can swap the game to your second monitor without having to swap display modes to move it over.
Use the Windowed (Fullscreen) display mode and while the game is in focus press Win + Shift + (Left arrow or Right arrow) to swap the program to the other monitor. If this isn’t working, go into Start → Settings → System → Multitasking → Make sure that Snap windows is enabled.