Hm, technically there is a finite number of options. What is the maximum number of characters for a character name...? ;)
In all seriousness though, I completely agree.
If you cant think of a name that works in English, try another language. German, Italian, and Latin all make good character names.
I had characters named "Shadowcat" "Hellcat" "Radiation" "Beautiful violent death" ... and that's just the ones I can remember off the top of my head, in other languages
The last one, I am particularly fond of her name. I may remake her, or if not remake her reuse the name for someone else... I digress.
Another great resource for character names is baby name sites. Not just for real names, mind you, but again delve in to names in other languages and you can find some names with really cool meanings that have a good sound for a superhero name.
Half of my characters have names translated to Irish Gaelic or Scottish Gaelic and a few German names. Just have to point people to your I.D. card if they ask (and you bother to put the English version there).