After Link brought the Triforce back from the Dark World, he gave it to the current king who was loved by many and considered a great ruler. Link soon after decided to set sail away from Hyrule.
However, when the king died the prince of the kingdom should have become king and inherited everything, but he could inherit the Triforce only in part. The Prince had searched everywhere for the missing parts, but he could not find them.
Then, a magician close to the prince, who is now king, brought him some unexpected news. This news was, that before his father, the king died, he had said something about the Triforce to his younger sister, Princess Zelda.
After learnign this the prince immediately questioned the princess, but she wouldn't tell him anything. After the prince, the magician threatened to put the princess into an eternal sleep if she did not talk, but even still she said nothing.
In his anger, the magician tried to cast a spell on the princess. The suprised prince tried to stop him, but the magician fought off the prince and went on casting the spell. When the spell was finally cast, Princess Zelda fell on that spot and entered a sleep from which she might never awake. At the same time, the magician also fell down and breathed his last.
In his grief, the prince placed the princess in the North Castle. He hoped that someday she would come back to life. So that this tragedy would never be forgotten, he ordered every female child born into the royal household should be given the name Zelda.