I'd look at covering that rock with a material or panels (fire retardant drywall?) that are rated as safe to be in proximity to a woodstove. Even if I had to redo the hearth to move the stove away from the wall a bit, it would be worth it to me to have a more neutral surrounding.

What to put behind woodstove

Thanks!! we are trying to stay budget friendly but I’m definitely going to look into that

Are all of the walls like this?

No.. this is just a corner of the room. I attached a photo of the room if you were standing in front of the wood stove :)