Lightning’s real first name in Final Fantasy XIII is Claire.
Lightning is the adopted name of Claire Farron, the pink-haired protagonist of Final Fantasy XIII. She takes the name “Lightning” as part of the hard, emotionally guarded identity she builds while trying to protect her younger sister, Serah. Her family name, Farron, is shared with Serah.
The English name reflects a localization choice. In Japanese, her real name is Éclair Farron, a name that also appears in the original version of the character’s identity. Because “éclair” is strongly associated with a pastry in English-speaking countries, the localized version uses Claire instead. Thus, Claire is the canonical English answer, while Éclair is the Japanese name.
Vanille and Fang are fellow l’Cie whose names are tied to major characters and events, but neither is Lightning’s birth name. Serah is Lightning’s younger sister, not an alternate name for her. Lightning first appeared as the lead playable character of Final Fantasy XIII, released in 2009, and later returned in two related games.