Greenwood the Great later becomes known as Mirkwood in Tolkien’s history of Middle-earth.
Greenwood the Great is the vast forest east of the Anduin. In the earlier history of Middle-earth it is associated with the woodland realm of the Elves and with the region later ruled from the halls of Thranduil. After the arrival of the Necromancer, Sauron, at Dol Guldur, a growing shadow corrupts the forest.
The name Mirkwood reflects that change. By the time of The Hobbit, the forest is dangerous, difficult to cross, and inhabited by giant spiders and other threats. Bilbo and the Dwarves travel through it during their journey to the Lonely Mountain, while the wood-elves capture the company after the travelers leave the path.
Mirkwood is not the same as Fangorn, the ancient forest associated with Ents, or Lothlórien, the Elven land west of the Anduin. Tolkien’s use of multiple forests can cause confusion, but each has a distinct location, history, and cultural identity.