One hundred days is really not enough time to name a child. Toph calls the baby “Badgermole” and would like to do so forever. “I’m almost tempted to name the kid after me.” Toph brushes the kid’s hair with a finger, breathing in the scent of milk and oil and baby.
“Don’t,” says Azula. “Naming children after living relatives is...inauspicious. Not to mention foolish.” In letters to Zuko she writes “baby” or “child” or “spawn.” At least, that’s what she says she writes.
Toph breathes in everything the child is, then suddenly, magically, breathes out the perfect name: "Lin."