Yavimaya, Cradle of Growth isn't a Forest while it's not on the battlefield.

Land cards not on the battlefield aren't Forests while Yavimaya is on the battlefield.

Yavimaya's ability causes each land on the battlefield to have the land type Forest. Any land that's a Forest has the ability "{T}: Add {G}." Nothing else changes about those lands, including their names, other subtypes, and whether they're legendary, basic, or snow.