I did when I was 6 and got my first Zelda game. I only had 1 file named Zelda that was stuck on Outset Island. After that I always named him Link because I then found out about Link.
No since I played Zelda as a kid I didn't mix it up. However I know many people who did mix it up and I can see why. I don't think Nintendo did a great job explaining to everyone. Though Legend of Link just doesn't sound good so it's probaly for the best.
Originally I had no clue what Link's name was... I happen upon this site and was like... "why are they keep saying Link" then it was like "Oh, is that little characters default name?"
But at that time I didn't even know who Zelda was... I was a loss little child.
No, it was fairly clear to me that Zelda was the princess. This might be because the first Zelda game I played was ALttP and Zelda introduces herself at the very beginning of the game. I also had my friend there to explain who all the characters to me.
Yeah me and my sister grew up playing the games around my dad so the confusion was cleared up very quickly. There are still many times where I bring it up to my friends and they are confused about the difference between Link/Zelda.
Never. When I first saw Zelda games, I didn't even know what they were called, as my cousin was the one playing. I asked him what the main character's name was, and he told me it was Link.