There's an Ada Mary Duncan registered in the first quarter of 1876, Hackney. I wonder if she was illegitimate?
Even more interesting, there's a George Dives in the 1881 census, aged 65, a widower, b. Nutfield, Surrey, in West Ham. His address is Distillery House No. 5, Short Wall (his occupation is Corn Miller). He has also an unmarried daughter, Helen Dives, aged 39, in the household.
Perhaps either George Dives was the father of Ada, or he was her grandfather - and not knowing her father's true details she used those of her grandfather when she married.