Should I do this for a girl?

I've been talking to this girl for about two months. We aren't dating because she said she didn't want to hurt her ex. But she gave me an ultimatum. She told me an her ex that whoever got her name tattooed on us first, she would date him. I don't know what to do. I'm sixteen and I'm sure my parents wouldn't let me. But I've known thi girl for five years and I really like her. What shoul I do?