The Bayer designations c Centauri and C Centauri are distinct.
The designation c Centauri is shared by two star systems in the constellation Centaurus: c1 Centauri (HD 129456) c2 Centauri (HD 129685)
The designation C Centauri is shared by three star systems: C1 Centauri (V763 Centauri) C2 Centauri (HD 100825) C3 Centauri (HD 101067)
See also γ Centauri Alpha Centauri C (Proxima Centauri) σ Centauri 3 Centauri