An excellent study called "A prospective psychological study of 50 female face-lift patients." by Goin MK; Burgoyne RW; Goin JM; Staples FR, (Plast Reconstr Surg, 65: 4, 1980 Apr, 436-42), showed that none of patients who had facelifts in their series, kept it a secret.
Twenty percent told their immediate family, 60% told all family members and close friends, and 20% told everyone .
(See also Goin MK, et al. Face-lift operation: the patient's secret motivations and reactions to "informed consent". Plast Reconstr Surg, September 1976.)