When playing co-op, next to most but not all (or everyone's sometimes) status (name, level, class) there is another word. Like Contemptible Killer, Shadow Ninja, Specialist, Sniper, Fox, Witch, etc. The one next to your name also appears down next to your own level/XP bar. It doesn't change for a person often, but will occasionally.
What do these names mean?
Best Answer
Those words are your character's title. The title is taken from the classmod you have equipped. There are over 100 different titles possible, so instead of writing out the whole list here, I will link to the lists of class mods on the Borderlands 2 wiki.
Commando
Siren
Gunzerker
Assassin
Mechromancer
Under Possible Skill Boost on those pages, the word in parentheses goes before the name of the classmod, so the title of a Commando with the first mod and variant on the list would be Front Line Engineer. This title replaces your normal class name.