There's also some other stuff, like the Shadowmoon medal, the package with it called him a Rival Rider. There was also the Super Climax Heroes site. Also, some promotion for All Riders vs Dai-Shocker called him an evil Rider. Still, it's inconsistent, and most of the time he's just "Shadowmoon".
Yeah, I don't think it really matters. It will disturb someone OCD with collecting "Evil Riders" though, lol.
He's a rider when Toei finds it convenient. Just like how he sucks ass in combat when Toei needs to make a new hero look powerful.
Shadowmoon being blasted out a thousand meters with a fugging Metal Shaft will forever haunt my mind.