To my knowledge, there are only two fighters currently active on Jazz Jackrabbit 2.

Fighter II and Fighter III are actually the same person. He also goes by the names Ascotti and Mazinkaiser (sometimes he'll replace kaiser with something like foo or dog as a joke.)

Fighter I is apparently new. I've never heard of him before.

There were fighters back in the Golden Days that were active on Jazz Jackrabbit 2, including one simply named Fighter, but they are long gone.

Fighter is a very common name and really not a good choice, but whatever fits. As long as it isn't "Firebolt" I'm sure no one will object. ;-P