Why did Alice lie about her name?

I thought Natalie Portman was the most redeeming character- until the end. Seriously, she lied to Jude Law the whole time? Why make up her name like that? For what purpose? And then we're supposed to feel sorry for her when he cheats? She didn't seem to be any better then the rest of them. She seemed like a pathological, emotional liar. Roberts was self-destructive. Jude Law's character reeked of a weak and very manipulative snake. And Larry was just bluntly evil- and sexist.