In the Pokémon TV series, the villainous organization led by Giovanni is Team Rocket.
Team Rocket is a criminal organization that seeks to obtain rare and powerful Pokémon. Giovanni, who also runs the Viridian City Gym for much of the original story, serves as its leader. Jessie, James, and Meowth are the organization’s most recognizable anime agents.
The trio repeatedly attempts to capture Ash’s Pikachu, but their plans usually fail and end with them being blasted away. Team Rocket is broader than the comic trio, however: the anime also shows other members, bases, experiments, and missions connected to Giovanni.
Team Galactic, Team Magma, and Team Plasma are different villainous groups associated with later Pokémon regions and storylines.