In Breath of the Wild, Link had a house in Hateno Village. That house, spoiler alert, still exists in Tears of the Kingdom. However, it seems that Link either gave the house over to Zelda for her to use it as the new owner sometime between the two games, or they suddenly started to shack up with one another. Regardless, Zelda is seemingly the primary owner, which is why you build a new house in this game.