According to Zelda II the Adventure of Link the King of Hyrule died and left succession to his two children a Prince and a Princess. The King had left the location of the Triforce of Courage in Zelda's hands and her brother power hungry as he was demanded to have it. Zelda refused and so the Prince brought in a wizard to try and get the information from her. When she still refused the wizard went overboard and over the Prince's objections cast an eternal sleeping curse on Zelda. The curse was so powerful that casting it killed the wizard (so one problem down). Zelda's brother was so distraught at what had happened to his sister that he declared all Hylean Princesses would be named Zelda from that day forth, so the tragedy would never be forgotten.
Bearing that in mind, what happens in the royal family if the King and Queen have two female children? Do they both get named Zelda and everyone is royally confused or is it like only the first born that gets the legendary name and the second born named Hilda is left feeling totally cheated out of an amazing destiny and goes on to try and steal the Triforce from another land.