Usually a nickname form of Fabiola or Fabián, from the Latin Roman family name Fabius, linked to beans.
Faby is usually a nickname form of Fabiola or Fabián, both connected to the Latin Roman family name Fabius. That makes it feel compact and affectionate, with the intimacy of a familiar short form rather than the formality of a full historical name.
As an independent given name, Faby has a bright, playful, and approachable quality. It sounds modern and informal, but its Roman roots give it a subtle depth beneath the simplicity. In use, it feels friendly and light, the sort of name that keeps its charm precisely because it does not try too hard.