Because this thread was bumped by someone editing their post from last year .. Deb, I grew up with my mum being called Sue by everyone (well, except those who called her Mrs Paul). I didn't know she had another name for years.
That doesn't make the name Sue any the less hers/her. She acquired Sue when in the WAAAF during the second world war. It stuck even after she was demobbed. It was really, REALLY strange many years later to hear her called "Ailsa" (or, often, "Ails by her sister-in-law). Many more years later and the only people who ever called her Sue were her WAAAF mates, with whom she got together once a year on the anniversary of their join-up date.
Maybe your gr-grandmum's "Sophia" was something like that. Margaret used to be Daisy, Peggy, Peg, Meg, Madge, Megan, Rita, Greta, etc, the only one of those even halfway relatable to Margaret might be Meg.
Anyone ever listening in to my husband talking to me would have thought my name was Honey.