Well, perhaps Harry could use magic to shape the island. He might create a magical forest filled with unique creatures from the wizarding world. He could also build a hidden school on the island to teach magic in his own way, away from the prying eyes of the Ministry of Magic.
Hermione could be there. She would be really helpful in planning and organizing the island. For example, she might set up a system for categorizing all the magical knowledge and resources on the island.
He might have discovered the island during one of his adventures and claimed it as his own. Since there was no one else on the island at the time, and he was the first to set foot on it and recognize its potential, he decided to make it his property.
In Harry Potter fanfiction, a character being 'his own man' might mean that he has the independence to make his own choices, regardless of the expectations of others. For example, a character might not follow the typical path set by the original story, like a Slytherin who decides to oppose the pure - blood supremacist views of his family.
Maybe Harry discovers a new and unique magic that only he can perform. This new magic could be the mark he makes. For example, he might find a way to combine different spells in an unprecedented way that gives him an edge in fighting the dark forces.
Maybe Harry, tired of the existing power structures in the wizarding world, starts his own empire. He could start by recruiting those who have been marginalized, like werewolves and half - bloods. He'd then use his fame and skills to establish a new order, one based on equality and true understanding of magic.
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.
In this fanfiction, Harry could be forced to create an island due to some kind of dark magic threat in the wizarding world. He uses his knowledge and the help of his friends like Hermione and Ron. They might design the island to have its own unique magical ecosystem. For example, they could create a special type of tree that produces potions - ingredients as its fruits. Harry could also make a school on the island for young witches and wizards who are in danger in the regular wizarding world.
Some pure - blood supremacist wizards could be antagonists. They don't like the idea of Harry creating a haven for all kinds of wizards on the island. They might try to sabotage the island's creation or attack it once it's made, fearing that it will disrupt the 'purity' of the wizarding bloodlines.