No, Link is a new person every game. He only kills Ganon[dorf] once as that person. It’s the nature of the legend- a hero who looks the same as the last hero, and has the same name, shows up and beats the reincarnating Gerudo leader and saves the reincarnating princess of Hyrule. Or thereabouts.

I’ve seen it explained once- each game does indeed take place in a completely different era (though sometimes the handheld ones apparently take place in the same timeframe as some of the main games, like Link’s Awakening having some sort of connection to Wind Waker, I think? I forget), and each Link is technically a different person and not reincarnated, while Ganon and Zelda may in fact be reincarnated on regular intervals. Keep in mind, though, I got this from a source of collected knowledge of various fans- a Zelda wiki, I believe.