Vanessa is a name that was created by the Anglo-Irish poet
Jonathan Swift for the title character in his long poem
Cadenus and Vanessa, published in 1713.
He named the character after a friend of his,
Esther Vanhomrigh. The first syllable is from the
Van in Vanhomrigh, and the last part is from
Esther.
If you want a "meaning" for
Vanessa beyond that, you can read the poem and see what the character is like:
http://www.readbookonline.net/readOnLine/3377/
There is also a genus of butterflies called
Vanessa, but they were named about a century after the poem by the entomologist Fabricius, probably after the character in Swift's poem. But I suppose women or girls named
Vanessa could use a butterfly motif if they wanted to link their name to a particular symbol:
http://images.google.com/imgres?imgurl=http://www.public.iastate.edu/~mariposa/images/americanlady20pc.jpg&imgrefurl=http://www.public.iastate.edu/~mariposa/species.html&h=307&w=410&sz=35&hl=en&start=12&um=1&usg=___vBnu0RDhcZyywwskdy-K33FJwg=&tbnid=uaAbQj7CAwKeIM:&tbnh=94&tbnw=125&prev=/images%3Fq%3Dvanessa%2Bbutterfly%26um%3D1%26hl%3Den%26sa%3DG