Yes, that confused me too. When I first read it, I thought that she had Link take the Sue's name (like how she called the king "King Zelda")

You're right, it makes no sense. But Link has to be known there so that the Sue can ride on his coattails and butt in on the action.

Really? I never knew that! I suspected that there was something going on, but I forgot to Google. ^^;