The only ones to be graced with custom nicknames in my forts are dwarfs with some outstanding military story. The names usually relate to the awesome act that earned them their names.
Such as:
Footbane - the first kill of the fort was this guy biting a goblin in the foot and thrashing it around until it bled to death.
Skullfist - One of my first militiadorfs, before I had made any proper weapons or equipment, killed three goblins in a row by punching them in the face and caving in their skulls through their brains. He had no combat or wrestler experience when this happened.
Captain Badass - One siege, a few trolls and a handful of goblin archers made it into my courtyard before I got the bridge up, my militia captain was first on the scene, while everyone else was gathering equipment. She blocked arrows right and left and hacked all of them up before anyone else managed to get there. She came out a bit worse for wear, but still managed to hold her own in later fights despite not being able to walk.
Cleaver - killed a forgotten beast in one hit due to decapitation. I later found this guy removing all of a human's limbs before finally chopping off the head. I'm a little scared of this one to be honest.
Headstrong - (one of my favorite stories) For some reason this unlucky guy was caught outside when a goblin siege showed up, he was already in the militia, but was off duty at the time. I had planned to just let him die, it was his own damn fault for being out there, but he didn't seem to agree with that. He ran out into the middle of three squads of goblin archers, and literally ran a circle around them, never getting hit once. He then headed north away from the archers where he was intercepted by a squad of speargoblins. They chased him around half of the map before they finally caught him, by which time the rest of my military had dispatched most of the rest of the siege. I sent a few squads to save this guy, having reconsidered letting him die after all that. He got stabbed in the foot and fell over unconscious, and lay there for three days before reinforcements arrived. Two speargoblins and one axegoblin spent the entire three days bashing this guy in the head, and failing to get through his masterwork steel helmet. He survived the entire encounter with minor wounds.
The only non-military dwarf to get a nickname is the poor sap that I send to open the candystore. I call that one "Sacrifice," though I will change their name if one ever manages to run to safety.