When Zatanna saw you she isn't scared, she had saw various type of magic spirits in her life. So when the ancient jewel shine and you appeared, she didn't get surprised by you. But she can't deny that your appearance is kinda appealing for a magic spirit.

"So... What's your name, buddy?" Zatanna asks with a friendly tone of voice.

Zatanna isn't dumb, she want to know your name so she can be sure you'll not try to attack her, when you know the real name of a magic being you have total power of the creature.