It was never mentioned who the first ever head gamemaker was, but for the 72nd, 73rd and 74th the head gamemaker was Seneca Crane. For the 75th games Plutarch Heavensbee is the head gamemaker.
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Senaca Crane was the head gamemaker for the 74th Hunger Games. He was hung after he allowed both Katniss and Peeta out of the arena.
In the first book, Seneca crane is the head gamemaker, and they refer to everyone else as "the gamemakers". the only gamemaker they refer to by name in the whole series, is the head gamemaker.
Her head stylist is Cinna
President Snow. He is also angry with Seneca Crane, the head gamemaker, for letting both Katniss and Peeta live. As a result, Seneca Crane is exectuted, and Katniss' life becomes controlled by Snow, making sure that she doesn't set off a rebellion, which she does.
Haymitch trains Katniss and Peeta in the first book because he is the only living past winner from District 12. All trainers must be winners from their district, but since there's only one, Katniss and Peeta have to share one.