Virginia was actually named Adeline Virginia Stephen. She was named after her own Aunt Adeline and her mother’s Aunt Virginia.
Virginia’s Aunt Adeline was her mother Julia’s eldest sister, who had recently died when Virginia was born. Julia’s Aunt Virginia was her mother Maria’s sister, Virginia Pattle who, incidentally had three daughters, Isobella, Adeline and Virginia and a mother called, guess what? Adeline. Gosh, I have never known of so many Adelines and Virginias.
However, the name, Adeline, reminded Julia of her sister too much and she decided not to use it. Adeline became known by her middle name, Virginia, and well, the rest is history.
Above is my trying to make sense of all the Adelines and Virginias. All the pink highlights are those two names. The pink circle is our Virginia of course.