My aunt Enid Louise was also known as Dolly. It seems her father, going away to serve in the Great War when she was a child, would sing "Goodbye, Dolly Gray" to her at each leaving, and the name stuck. Another aunt Dorothy who might have been known as Dolly, was always known as Paddy - only a nickname. However, a Eugenie in my tree seems to have settled for Dorothy. There's no accounting.
Some short forms seem to bear no relation to the original name. I had aunts Elizabeth who were Cissie and Bunty, but I'm assured these are genuine pet forms and not nicknames. Elizabeth to Lucy, though not usual, seems reasonable on this basis. Chris