I don't think it necessarily has to match, but if you are able to obtain the same stone then you certainly can't go wrong by using the same stone on the fireplace

What is the name of your stone kitchen backsplash? Really pretty! It would look amazing as a fireplace as well!

I would use the same stone...it's modern and today, and there isn't that much of it. Trim out the fireplace from the edge of the new stone to the corners of the walls and paint the same white as the mantle.

Can you continue the hardwood/laminate that is in the kitchen, because that would look perfect. If not, I would consider using something as dark or almost as dark as your kitchen cabinets. I would not use anything light colored such as the stone backsplash. Let that stone stand out on the fireplace. Then look for a very large rug for that area that is light in color on the background, but a large pattern with colorful reds or bright yellows, greens, blues, etc., whatever YOU like. Let the rug anchor the space then use those bold color for accents, large pillows with stripes, large artwork, etc.