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:
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: