It's just a bit of fun at first, letting Jack believe she's Christy. After all, he was nuts about her before she said au revoir to England. And when he asks Annabel out, the fun becomes something even more interesting. The more they date the deeper they fall for each other. So
what if Annabel has to fib a little to keep up the façade?
As the lies start compounding, and she realizes that they're falling in love, she has to tell him who she really is. But she'll lose the love of her life if she does.