The region in Pokémon Legends: Arceus is called Hisui.
Hisui is the historical setting of the game and is presented as the land that later becomes known as the Sinnoh region. The story takes place long before the events of Pokémon Diamond, Pearl, and Platinum, when human settlements are still developing and people have limited knowledge of Pokémon.
The player joins the Galaxy Expedition Team and helps create one of the earliest Pokédexes. Hisui contains distinct environments such as Obsidian Fieldlands, Crimson Mirelands, Cobalt Coastlands, Coronet Highlands, and Alabaster Icelands. Several Pokémon also have Hisuian forms or evolutions.
Sinnoh is therefore a related but different answer. Sinnoh is the later name used in the modern-era games, while Hisui is the historical region’s name in Legends: Arceus. The game was released worldwide on January 28, 2022, for Nintendo Switch.