It was first called Hyrule Fantasy in Japan, the western version was called Legend of Zelda. After some time, Japan used the Legend of Zelda IP by default as well. If you are familiar with the canon lore behind the franchise, Zelda is the human incarnation of the Goddess Hylia and is reincarnated over time. Much of the legend surrounds her.

Link holds the spirit of the chosen hero of the Goddess, and is also reincarnated. He is merely a tool (an important tool) of the Goddess and nothing more.

The canon games that do not have Zelda present are side stories that follow an incarnation of Link in a Quest after his initial adventure regarding Ganon and Zelda. They use the same IP Legend of Zelda to signify that it is a canon entry in the Legend of Zelda franchise, despite Zelda not being present for these side stories.

Hope this clears things up.

Yeah, but does he have any character? Feels more like an empty husk that could be replaced with anyone else to me.

Serious reply: Because Miyamoto liked the name "Zelda". He named the princess after Zelda Fitzgerald, wife of author F. Scott Fitzgerald, and he probably liked the ring to it so much that he decided to name the whole game after her.

Samus is the same way but a character none the less. Link is a character now. He has a history, he has a story, he has a name.

Why does the herpes medication have to be called Herpecin?That's some scarlet letter bullshit right there. My friend from Niagra Falls was really mad about this.

Because a game doesn't have to be named after the main character, Zelda is the central figure everything revolves around as each incarnation of her is the reincarnation of the Goddess Hylia who triggered the Tri-Force cycle and as explained in Zelda 2 anytime the is at least one Princess in the royal family they're named Zelda to honour one of the earliest Royal Princesses who passed away.

LOL HAHA. I just laughed so hard at this. I imagine a girl finding that in her BFs medicine cabinet xD

He does have character in BotW, you have to search for the background story though.

In Zelda's diary she states that she feels like Link looks down on her for her failures because he is so quiet and reserved.  One night, she asks him about it and he tells her that it is due to the constant pressure his role puts on him.

He is the chosen Knight to guard the Princess.  He pulled the Master Sword and is expected to save everyone.  Everyone is counting on him, and he is viewed as a becon of hope.  Due to this, he fears letting everyone down.  He feels like he cannot show his emotions as if he showed how scared he really was, people might lose faith in him.

Because of this he internalized his feelings and speaks only when necessary (like when he motions like he is explaining something or you select a dialog option).  This would allow him to remain strong in the eyes of t  he people.  It is also implied that behind the scenes, he cared deeply for Zelda and they opened up to eachother as their quest went on.  While their actual problems may have been opposite to one another, they actually mirror eachother in the the grand scheme, so it is quite fitting actually.

Link has a name, he has a personality, and has been around as an icon for over 3 decades.  It might not have been the original intent, but Link is very much a character now.  BotW only makes it even more apparent than ever before.

The diary I speak of can be found in Zelda's room (one in her study as well), you should check it out sometime.

Sadly I haven't played BOTW that far. If he really became a character I'm interested to see what future Zelda games will become.

While Link is the main character, he’s not generally a well established character in the universe. His backstory is usually left vague, he doesn’t have a real personality, he’s just the “link” between the player and the game.

Zelda, traditionally, is the ultimate goal of the player, whose plight really drives the entire story. Not always, but I think this holds true for at least the classic games in the series.