Well, actress Vivica A. Fox (the A stands for Anjanetta) pronounces her name as you're pronouncing it. To me, it sounds very harsh. I much prefer Vivian / Vivianne or Vivianna.
Deliberate cruelty is unforgivable, and the one thing I've never been guilty of. - "A Streetcar Name Desire"
That's how I noticed the name - I was watching Ella Enchanted, and saw her names on the credits. I've seen Kill Bill, but the name never registered before.