OK, I'm just gonna put this out there: Linkle is not a Link. Her timeline already has it's link so she must be something else right? I put it to you that Linkle is not related to the hero but another recurring from the Zelda time line: Tingle!
First lets examine a few things about her design. Yes, she wears green like the hero, but in no way like the traditional tunic and cap, what she does wear is a green hood and orange bottoms, not too unlike Tingle with his hooded leotard and red shorts.
Then let's look at her weapon of choice. Now you would be hard pressed to associate a weapon with Tingle (aside from perhaps bombs if you had the gba adapter) But I would say that the weapon you would most connect Tingle with would be the bow since it's the weapon you would always use when you wanted to talk to Tingle in his game of origin. And Linkle uses a form of bow as her default weapon (with bomb arrows thrown in just to reference the bombs mentioned earlier)
Then, let's consider her "heirloom" the compass. She is sure it belonged to the hero. Which it could have, but it could just as well have belonged to someone who, as a maker of maps, would need a compass. Further she wears it around her neck Just as Tingle always wears his clock.
Now the name. In both English and Japanese, Linkle's name follows the same naming convention of Tingle and his brothers. a family Tradition perhaps?
And lastly their character, or at least one driving character trait: Delusion/obsession with the hero. In all the games he appears, Tingle is obsessed with the hero, instantly insisting on being best friends with them upon meeting. Further in all his appearances, Tingle is sure that he isn't just some normal guy but he must be a reincarnated fairy. This parallels far too well with Linkle's obsession with legends of the hero and insisting that she has to be the hero reincarnated.
Even tho she was first conceived as a female counterpart to Link, I think when fully developing the character they decided to go another way. What if the obsession for the hero was passed down through the Tingle family until one generation a descendant decided that they them self must e the hero? I just hope for her sake she never fully learns her real origins in the Zelda universe.