When i was younger we had legend of Zelda 1 and 2. Since the second one was called adventures of Link, I always knew his name was link. I correct the silly people who think that Link is Zelda. It has always seemed straightforward to me.
When I was about 5 years old and I watched my older brothers play OoT and for probably a month of watching and playing I thought Link's name was Zelda even after all of the times my brother's corrected me. Zelda just felt right because he was doing all of the work in the game so I thought he deserved to be in the title.
Considering the fact that I have an aunt named Zelda, I definitely never thought it was Link's name at all... although I remember that some of my friends couldn't seem to get it straight as to which character was which, even after beating some of the games.