The name: Commander.
Although this is my idea and I think it's cool, I also think it would not work in Doom.
The story: A WW2 British commander. Known for his strategical skills, he was sent to fight the Nazis, by commanding a squad of elite British soldiers.
I think this would be rather cool. Except we already have a "military" type class. The DOOM Marine.
Anyway here are my ideas (not overly descriptive):
HUMAN:
Ninja.
Uses a katana, shuriken, and smoke bombs (for those melee lovers out there).
When standing still against a wall, he becomes slightly transparent (blends in).
He runs rather fast, not as fast as the Hunter, but fast. He also jumps high and is very agile. He has average health.
Duke Nukem.
Uses his shotgun, ripper, pipebombs, and his trademark jetpack.
Although he is well armed, he moves slower than average, not quite Cyborg slow. When he uses his jetpack he flys like Sjas, but it uses fuel faster than Cyborgs. He also has multiple taunts, each time you taunt it selects a random DN3D one liner, from a pool of ten. He has slightly above average health.
GHOULS:
Hephaestus (Greek god of Fire + Metalworking).
Has fire breath, (think Bowser) fire balls and can bite.
Pretty much a fire version of Frostbite. He also has the unique ability to hurt people he's close to, due to his fiery body temperature. He looks similar to a Lost Soul from DOOM.
And that's all I got. Yes, only one ghoul idea, ha, ha!