Yes you can paint the fire resistant material behind the wood stove but you should paint the fire resistant material with high temp paint that is made for high heat applications although your fire resistant material should not get that hot.
Your wood stove should have a heat shield built onto the wood stove if it's a modern store bought wood stove so the wall although it may get warm it should not get too hot.
You could paint it with regular paint but if possible I would paint it with high temperature paint to prevent the heat from peeling or chipping the paint.