These are all of the Gym Leaders from Pokémon Yellow Gamma Yγ
A Gym Leader (Japanese: ジムリーダー Gym Leader) is the highest-ranking member of a Pokémon Gym. The main job of a Gym Leader is to test Trainers and their Pokémon so that they are strong and resourceful enough to compete against the Elite Four in the games or the Pokémon League in the anime. If a Trainer defeats a Gym Leader in battle, then the Trainer earns that Gym's Badge.
A Gym Leader's job is not just to test upcoming Trainers. They must oversee how their respective Gym is run and to maintain it. Great care must be taken to make sure that their Gym reflects the best environment for the Pokémon type and playing style of choice, usually an environment that suits that type of Pokémon used there (like pools in a Water-type Gym or flowers and plants in a Grass-type Gym). According to Morty, teaching young people how to battle with Pokémon can also be the job of a Gym Leader.
It has not exactly been made clear how Gym Leaders attain their position, but it appears that it varies for each Gym. Some of them founded their Gym and are self-appointed; others, such as Whitney, are chosen by the other members of the region's Pokémon League. A few appear to be passed on through families: Janine, Falkner, and Flannery all take over their respective Gyms from a close family member. However, Gyms do not necessarily belong to a particular family; Roark and his father Byron are both Gym Leaders at the same time, in different Gyms. Leaders can also choose to vacate their position; examples include Koga, Giovanni, and Wallace.
Brock (Japanese: タケシ Takeshi) is the Gym Leader of Pewter City's Gym, known officially as the Pewter Gym. He gives the Boulder Badge to Trainers who defeat him in battle. He specializes in Rock-type Pokémon.
Misty (Japanese: カスミ Kasumi) is a Gym Leader of Cerulean City's Gym, known officially as the Cerulean Gym. She hands out the Cascade Badge to Trainers who defeat her. She specializes in Water-type Pokémon.
Lt. Surge (Japanese: マチス Matis) is the Gym Leader of Vermilion City's Gym, known officially as the Vermilion Gym. He hands out the Thunder Badge to Trainers who defeat him. He specializes in Electric-type Pokémon.
Erika (Japanese: エリカ Erika) is the Gym Leader of Celadon City's Gym, known officially as the Celadon Gym. She hands out the Rainbow Badge to Trainers who defeat her. She is a serene young woman who specializes in Grass-type Pokémon. She sometimes dresses in elegant kimonos and seems to represent traditional Japanese beauty.
He was promoted to a Master Poison-type Trainer and became a member of the Indigo Elite Four some time after the events of Generation I and its remakes, but before the events of Generation II and its remakes, thus leaving his daughter Janine in charge of the Fuchsia Gym.
Sabrina (Japanese: ナツメ Natsume) is the Gym Leader of Saffron City's Gym, known officially as the Saffron Gym. She hands out the Marsh Badge to Trainers who defeat her. She is a young lady with psychic abilities, and thus trains Psychic-type Pokémon.
Blaine (Japanese: カツラ Katsura) is the Gym Leader of Cinnabar Island's (later the Seafoam Islands') Gym, known officially as the Cinnabar Gym. He hands out the Volcano Badge to Trainers who defeat him. He is a highly intelligent man who uses Fire-type Pokémon.
Giovanni (Japanese: サカキ Sakaki) was the head of Team Rocket, and served as the secretive Gym Leader of Viridian City's Gym, known officially as the Viridian Gym. He handed out the Earth Badge to Trainers who defeated him. As a Gym Leader, he specialized in Ground-type Pokémon, but his master plan includes collecting rare Pokémon of all types. He is the only character in the games to have the Trainer class Boss'FRLG/Rocket Boss'HGSS (Japanese: ロケットだんボス Team Rocket Boss).
(Giovanni is avaliable too Team Rocket Yγ )