Vanessa was invented by Jonathan Swift around 1708 as a literary pseudonym for his beloved Esther Vanhomrigh — combining "Van" (from her surname) with "Essa" (a pet form of Esther).
Today Vanessa is widely used across English- and Spanish-speaking countries, sitting in the U.S. top 250.
Vanessa does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Vanessa reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.