So he's a Soviet not a Russian? I know there's a difference. What are the Russian words for "champion, patriot, or soldier"? No offense but "Nameless Soldier" doesn't really sound like something little Russian kids would want on their lunchboxes.
I mean no disrespect in your country's monuments to the fallen dead. I just hate to see a good character pass up a better name. How about Red Soldat? It's just a suggestion but it sounds stronger for a superhero I think.