The name of the main playable character in the Legend of Zelda series is a boy named Link. Link is often given the task of rescuing Princess Zelda (the main female character).
What is the Main Character’s Name in The Legend of Zelda Games?
Some people mistakenly refer to the main playable character in the series as “Zelda”. This an error. The confusion is most likely due to game’s title and the confusing introduction to the popular original NES game. 
Perhaps in an effort to clarify the confusion, the names of the second and third games Zelda II: The Adventure of Link and The Legend of Zelda: A Link to the Past both included Link’s name.This video discusses the history of the Legend of Zelda and some of the more interesting facts about the series.
Is Link a Boy and Zelda is a Girl?
Traditionally Link is a boy and is the main protagonist who saves a girl named Princess Zelda.
Why Didn’t they Just Call it “The Legend of Link”
When released in 1986, the original Japanese version was subtitled “The Hyrule Fantasy” (the series’ main location is the fantasy land of Hyrule). It was changed to the Legend of Zelda in the North American version for unknown reasons, although one could speculate that perhaps the translator was simply one of the first to make the Legendary Zelda error. 
The series has had number of translation errors and mistakes over the years.