"My" Constance (Cissy) Wilson was not her real name, but was only used on the birth certificate of her son in 1913 - to hide (forever her solicitor hoped) her real identity.
Cissie Wilson was the name she gave herself, or the family solicitor J Ingram Dawson gave her, to hide her identity when she became pregnant in 1912. Her name was in fact Constance and her grandfather had been a Wilson, but was required to change his name to marry Cissie's grandmother.