Sometimes it takes me a bit to come up with a name I like if my original thought is already taken. There are no limits to the number of names available, but it can take some modification and imagination to create one that has not already been taken.
For myself, back in the original CoH I created synonym and word lists associated with different powers and/or concepts. Now just applying synonyms does not always cut it (if I want Fireball, Incendiary Spheroid is just not a suitable replacement :) ).
So I added titles to the list (e.g., The Mighty, the Amazing, Captain, Lord, Lady), or choose parts of words to combine with others to capture the concept. Sometimes the powers don't come into play, but the personality of the character (courage, protection, fighter, etc.).
In the old CoH, I wanted to name a character Atomstrike. Somebody else beat me to it. I ended naming him Atomstryke. On Homecoming, I recreated him as Atomstryke right out of the box, not even attempting to name him anything else. It had character (pardon the pun), so I stuck with it.
This is a long-winded way of saying there are a lot of options for naming; you might just have to apply a little extra creativity to it (which does not mean one has to get silly, unless you want to. :) )