You're probably not going to find many completely original games. Single-word names like Raven and Punisher are practically all gone. If I were you, I'd aim for one of two things:
A) Mashed-up Names - That is to say mashing words together to make a name that sounds good. For example, Metroid originally came from mashing the words Android and Metro (as in a subway) together to evoke the idea of sci-fi technology in an underground environment.
B) Plays on Existing Names - Sure, the name you want is taken. But that doesn't stop you from using them as a starting point to make your own. Whether directly using synonyms (NovaFlame from Starfire, Alicia Snow from Emma Frost, etc.) or using the name as a stepping-stone to something else (Songbird from Black Canary, Arachnid from Black Widow, etc.)
In the end, even with those methods, chances are painfully high that you'll end up with some D-lister that nobody knows. If that's the case, simply come to terms with it. Even the official comics give multiple characters the same name (For example, there are four different Flashes). Simply distinguish yours by making them a unique character. Don't let your idea go unmade just because somebody beat you to a character name.