jabraun
While I don't know of any particular gunstock carver, a quick google search shows different types from laser to the old fashioned wood carver beauties.
I don't know if anyone would have issues carving in a registered trademark name such as John Deere, they should or you should get permission perhaps from Deere, but if you were to do it yourself... it might mean more to your grandfather, and you'd bypass having a professional possibly infringing on that Marque.
Look up Joe Cummings, Bill Janney or Kirk Ratajesak (first three names that popped up) online to see their wares. Might contact them and see if perhaps they can lead you down a better road than I. Hoping there are members here who carve as well and can offer sage advice.
I will say, it is a really cool idea for a gift.