It's too good a nickname not to use. Concept stolen blatantly from Kimberly T.'s story The Turning Point.
Zuko turned long-sufferingly toward the earthbender, leaving his hand holding the ladle poised over the cooking pot. "Yes?"
"Why does Sokka call you Scarface?"
There was a long, awkward silence around the campfire. Finally Zuko spoke.
"Because I have a scar on my face." There was an unspoken 'duh' tacked on to the end of the sentence that made Toph frown.
"No kidding, Sparky. But Sokka wouldn't give you a nickname like that for a weeny little cut."
Zuko's voice was low but audible.
"That's because it's not little."
Toph appeared to think that over for a moment, and then she stood and marched over to Zuko. The prince hastily put the ladle down and began backing away, sensing her intention, but the girl moved her hand and a small protrusion of earth handily found his foot and he fell over backward. Toph hauled him up to a sitting position, and, ignoring his protests and clamping his arm in her stone-like grip to keep him from wiggling, began running the fingers of her other hand over his face. Zuko went stiff, scowling deeply, but he sensed that the battle was lost and the best course of action was to accept defeat gracefully. The rest of the party was watching breathlessly, likewise frozen in place. For a long moment the only movement was of Toph's hand as she traced the ridges and scabs of Zuko's scar. Then her face turned soft with surprise and she let her hand fall.
"Does it hurt?" she asked in a voice that was slightly smaller than her normal tones.
"Not anymore," Zuko said in an equally low voice. Toph appeared to think this over, and then said,
"Is that where…?"
She was silent again, and then her face lit up in its customary grin and she boomed out in her normal voice, "Man, Sparky, I had no idea you looked so badass. If this whole defeating the Firelord thing doesn't work out I could probably get you a job in the Earth Rumble."
Zuko shook her off, and the atmosphere around the campfire seemed to deflate.
"Yeah!" Sokka agreed, gesturing wildly with his spoon. "I know I'd pay to see the snot kicked out of you, Scarface."
"You'd be wasting your money then, Ponytail Guy."
The conversation devolved into an argument about Sokka's nicknaming abilities versus Zuko's, and if anyone had noticed that Toph had spent just as much time feeling the other half of Zuko's face, no one said anything.