[TheFightingHellfish]

I agree with Marsupial, and don't let them kid or intimidate you with all kinds of names.
American Walnut is Black Walnut, is Virginia Walnut, is walnut canaletto, or sometimes Black Hickory; 'Juglans Nigra'. All the same. The heartwood matures into a rich dark brown with sometimes wavy or curly grain, texture is generally coarse but uniform.

European Walnut, French walnut, lebanese walnut, etc. are all 'Juglans Regia' and tend to be less warm in color and more highly figured. It is the favored wood for most high grade gunstocks because of its stability and density.

'Burl walnut' is made from an almost cancerous growth near the root of some trees, is generally very dark and very highly figured. Because of its scarcity, burl is usually only used as a special trim wood or inlay.

The missing stripe on yours could be very easily fixed with American or Black walnut (the same). Most veneer products will only use the heartwood, which is darker than the sapwood, so your color should match well, and the grain in your photo seems like it shouldn't be too difficult to get a 'good enough' match.

I have tried the plain veneer, and the 'self adhesive' kind. I prefer the untreated, non self-adhesive kind and apply it with contact cement, usually 'pinning' the ends with something stronger (like gorilla glue) and clamping them until it dries, even if it means a rope with a half-hitch to clamp it right.
Is the veneer loose on either side of your split? If so, now is the time to fix it, just tap your fingernail down along the edges and listen for the 'pop'. Loose veneer will make a distinct sound. Just lift the loose spots Gently with a razor blade and work some glue underneath with a small brush or a piece of paper. For lifted areas too deep for you to get a brush into without further damage, a srynge with an 18 or 20 gauge needle (these suckers are BIG, usually for horses etc, but most pharmacies usually have them) filled with 85% Elmers and 15% water will get the glue safely under the veneer 'bubble'. Oh, and make sure to use the kind with a Screw On tip -voice of experience...
Then simply clamp or press it down with weights (Saran wrap keeps the glue from sticking to your clamps or weights.)

Edit: It will probably come rolled up like a poster, so when you uncurl it, be careful and slow -let it fully warm up before you unroll it. You don't want to crack it across the grain if you can avoid it. If it is not the self adhesive kind, the steam from a clothes iron or a tea kettle lightly applied may help.