Fun Zelda fact: The Zelda Timeline is by no means solid canon. But, if taken at face value, the titular "Minish" from The Legend of Zelda: The Minish Cap exist in every timeline. This is due to Minish Cap's placement directly after the events of The Legend of Zelda: Skyward Sword. ▼
Fun Zelda fact: Zelda is actually the princess, not the character you play as. That character's name is Densetsu.
Precisely! The game is named 'Zelda no Densetsu,' so you're playing as the densetsu.
If you want to name him that and place that burden on his shoulders... that's your perogative. However, fading into history is a critical part of Link's character. His work is thankless. In some cases, his victories never happened - and that is the greatest victory of all. ▼
See, I'm fairly confident that 'Link' refers to each game itself; for example 'A Link to the Past' or 'A Link to the Future,' suggesting that each game is a link in an overarching chain of the franchise.