There's no wrong reaction here. Soldat expects a lot worse than a little anger with no proper outlet. Tamping himself down is one of many possibly reactions, and not even the best one. "You can if you want, it doesn't. It doesn't bother me. But I go by Soldat now."

And. Steve probably knows exactly what that word means, actually, a thought that makes them wince, and explain weakly, "I know it's not much of a name, but it's what I chose, back when I didn't really know better. Just needed something to tell civilians so they wouldn't get upset. And now it's really mine."