Land of Whirlpools and Waves

This is a map of the shinobi world and this is an image of the Land of Waves.

There are only two islands near the Land of Fire which are both to the east and since the Great Naruto Bridge connects Waves to the Land of Fire horizontally, it should be the closest island in the east.

As such, the island of the Land of Waves appears to be the same one indicated to be the Land of Whirlpools.

The Land of Whirlpools was home to the Uzumaki Clan, a clan descended from the Sage of Six Paths and the foremost experts of fuuinjutsu. After the hidden villages were formed, the Uzumaki Clan created Uzushiogakure by taking small clans and families under their wing to increase their power base. They had a strong alliance with their distant relatives, the Senju, but chose to keep the island nation as their home rather than move to become a part of Konoha. The Uzumaki were essentially the rulers of the Land of Whirlpools.

But their prowess with fuuinjutsu caused them to become greatly feared during the Shinobi World Wars. This was only exacerbated by their willingness to share their knowledge with the Senju and their unusually long lives which armed their elders with the greatest well of knowledge and experience for the art.

By the end of the Second Shinobi War, Uzushio and the Uzumaki were destroyed. The survivors were scattered as they fled their homeland, fearing that the rest of them would be hunted for their knowledge. Kushina, fortunately, had already been sent to Konoha become the Nine-Tails Jinchuuriki but the loss of her homeland and family was a terrible blow.

The Land of Whirlpools was left ravaged and bereft of all leadership and shinobi.

Eventually, the island nation began to recuperate as victims of war sought out a land that would keep them away from conflict. Without Uzushio, the Land of Whirlpools held little value and was far enough out-of-the-way that there was no reason for shinobi to be there. As the settlers came and built atop the ruins of the hidden village, the island was renamed the Land of Waves to signify its new beginnings.

It actually managed to become a prosperous, little country through its shipping industry. But this changed when the wealthy shipping magnate, Gatou, seized control of their shipping through money and violence. He gained a monopoly on all business traffic and the entire country entered poverty, including the feudal lord.

But a year later, Gatou was killed and a bridge was built from the Land of Waves to the Land of Fire which served as a major boost to the economy. The country managed to become more prosperous than ever before.