In The Hobbit he is simply called the Elvenking. When Thorin Oakenshield and his party of Dwarves enter northern Mirkwood they are captured by Thranduil's elves and locked up when they refuse to divulge their intentions, before being freed by Bilbo Baggins.
Thranduil was son of Oropher and father of Legolas. In The Lord of the Rings, The gradually-established friendship between Legolas and the Dwarf Gimli, the son of one of Thorin's band, helps to reconcile the differences between Thranduil's people and the Dwarves.