No, I knew from the start that Zelda was the princess and Link was the hero. I can see how people might think Link's name is Zelda, that being the name of the series and all, but it's mentioned at least once in almost every Zelda game that the princess is named Zelda, and it wouldn't make much sense to have two characters named Zelda. On the back of the game boxes, it usually says something like, "Join Link on his most epic adventure yet!" or, "Play as Link while you travel across Hyrule." They don't put the name of the main character there for no reason whatsoever!
And I'm going to restrain myself from ranting about how some people still can't get his name right, even when they are informed that his name is Link.