He's Red, and she's Bronze, and neither ever asks for a real name. They pass warnings to the other about what cities to be careful in, and who to avoid stealing from because they'd recently taken something of theirs. He binds her hand when they take the smallest finger for getting caught in the wrong place with the wrong item. She stitches the worst gashes from being run out of a town with rocks.
The second time they take a finger, they take part of her hand with it, and he's half a world away. The next time he sees her, she's hungry and furious and has a grimy sheet of parchment with a design on it to replace what she's lost. He helps her get the pieces made, and put them together, because it means she owes him a favor he can call in later.
He doesn't expect to drag her, irritated and half-unwilling, from the mountains of Harad to Erebor to discharge her debt by helping Fíli. He never expected to survive the quest, and expected even less to find himself willing to involve himself with Thorin's kin. But he did, and he does, so he will use whatever resources he has to do so.
Even then, though, he doesn't ask her name, and he doesn't tell Fíli what to call her - she'll tell him what she wants him to call her, and whatever it is, he doubts it will be her real name. Unless she's being very generous, and then he'll have to reciprocate, because he knows Fíli will tell him.
When she finds him after the job is done, she watches him for a long moment before saying, "Nerthus."
"Nori." He frowns a little, wondering why she's telling him her name.
"If I ever see you in my workshop, I'll break your toes." It's not a hollow threat from her, and Nori raises one braided eyebrow curiously. "I'm not going back to Harad when there will be work enough here."