Since Link is a character in the Zelda universe, he reincarnates just like everyone else. It's just how life, death, and rebirth function in the Zelda universe. Give any dead person so much time, and they will eventually be reborn into a similar body with a similar name.

Why does Link and Ganon reincarnate?

Ganondorf has only ever been reincarnated twice, in FSA and way before BotW's oldest backstory, and we know very little about those incarnations before they became Ganon apart from his FSA incarnation being a Gerudo male. The reason Ganondorf has only reincanted twice is because he keeps cheating death.

Why is Link always named Link?

“Link's name comes from the fact that originally, the fragments of the Triforce were supposed to be electronic chips. The game was to be set in both the past and the future, and as the main character would travel between both and be the link between them, they called him Link.”