In Final Fantasy IV, the summoner who joins Cecil’s party is Rydia.
Rydia is the young survivor of Mist, a village inhabited by summoners. Cecil Harvey and Kain Highwind arrive there carrying a Bomb Ring, unaware that it will unleash monsters and destroy the settlement. Their earlier battle with the Mist Dragon also results in the death of Rydia’s mother, making her initially hostile toward Cecil.
After Cecil protects Rydia from Baron’s soldiers, she reluctantly travels with him. Her abilities make her unusually versatile: she uses both black magic and summons, while her early-game white magic is later replaced by stronger offensive spells after her time in the Feymarch, the Land of the Eidolons.
A common mix-up is confusing Rydia with Tellah, who is a sage and temporary party member, or with Rosa, a white mage. Rydia also temporarily leaves the group after Leviathan takes her to the Feymarch, but she returns later as an older, more powerful summoner and remains central to the story.