In the fanfiction, he might own a building that is actually a magical library. Since Harry has always been interested in knowledge, this building could be full of rare and ancient magic books. It could also be a place where wizards and witches from all over come to study and research, and Harry, as the owner, would be in charge of protecting these precious knowledge resources.
Maybe he buys an old, mysterious building full of secret passages like a wizarding manor. It could have a hidden attic with ancient spells and a cellar where strange potions were once made.
He could turn it into a training ground for young wizards and witches. Teach them how to defend themselves against the dark arts, just like how he was taught at Hogwarts.
Perhaps it's a community building. Naruto is a very community - oriented person. He could own a building that serves as a place for the villagers to gather, like a community center. There could be a cafeteria, a place for kids to play, and rooms for meetings and celebrations.
Perhaps it's an island with a hidden wizarding school, similar to Hogwarts but with its own distinct features. There might be ancient spells protecting the island, and the architecture could be a blend of different magical styles. Harry could have discovered this island during one of his adventures and decided to make it his own. He might use it as a sanctuary for those in need or as a place to study and preserve rare magic.
Well, perhaps it's a planet with its own system of magic. It might have a core made of pure magic essence which gives power to all the magic on the planet. And there could be different regions, like one area filled with floating islands where powerful wizards live.
He might want a place of his own, away from the chaos of Hogwarts and the wizarding world's constant threats. A building could be his private sanctuary where he can relax and practice magic without being bothered.
There's also a possibility that it's a Chinese Fireball. These dragons are very beautiful and powerful. In a fanfiction, the author might choose this type of dragon for Harry Potter to own because it would add an element of exoticism and grandeur to the story.
Well, it could be a magic item shop. Since Harry Potter is from the wizarding world, he might sell things like wands, potions, or magical artifacts in Konoha.
He could transform the building into a ninja academy annex. Naruto loves teaching and passing on his knowledge. In this annex, he could offer advanced ninja training, focusing on things he has learned from his own experiences, like dealing with powerful enemies and using the power of friendship and determination.
It could mean he has the rights to certain fan - created stories related to Harry Potter. Maybe he's a collector of unique fanfiction works, or perhaps he's in a position to manage or curate a collection of such writings.