Its according to the wood type. If it is indeed walnut, you can strip it, sand it smooth, apply a stain, then sand it lightly to be rid of the raised grain, and apply a new finish. Aniline dye stains are the best for this, not water based.
Most all manufacturers stain their walnut, even Winchester, who had a proprietary color they used, which was a reddish brown. Some even use a filler, before the finish, which is like a thin mud wiped into the pours.