The subject of this article has no official name. The name currently in use is a fan designator; see below for more information.
Cosmic duo is a fan term for the Legendary duo of Alola that consists of Solgaleo and Lunala. Solgaleo is an emissary of the sun known as the "beast that devours the sun". Lunala is an emissary of the moon known as the "beast that calls the moon". Both Pokémon evolve from Cosmoem, can create Ultra Wormholes, and with the power of both Pokémon, can create Cosmog. When grouped with their pre-evolutions, they are also referred to as the Cosmog line.
Solgaleo's signature move is Sunsteel Strike, a damage-dealing Steel-type move that ignores the target's ability. Lunala's signature move is Moongeist Beam, a damage-dealing Ghost-type move that ignores the target's ability.
Spoiler warning: this article may contain major plot or ending details.
In Pokémon Sun and Moon, Lillie takes care of a Cosmog named Nebby, which she fled from Aether Paradise with in order to save it from the Aether Foundation's experiments. Lillie keeps Nebby in a bag as an attempt to both keep it safe and to keep it from sight. Lillie and Nebby are eventually kidnapped by the Aether Foundation, and Lusamine takes Nebby and uses it to open Ultra Wormholes. Nebby then evolves into Cosmoem. Later, when the player and Lillie play the Sun and Moon Flutes at Altar of the SunneS/Altar of the MooneM, Nebby evolves into SolgaleoS or LunalaM, which is then caught by the player. It is required to catch it.