Use her name. As they are not married, and have no plans to be right now, the baby is primarily her responsibility. If, at some point, they do decide to get married, Ashley's maiden name can become the child's middle name, perhas, and both Ashley and baby can change their names at the time of the marriage. But as they are both young, and so much of the future is up in the air, I'd go with her last name, and if that upsets the father, well, he can "make it right" when he marries Ashley some day if they choose to do so. If they were bth ten years older than they are now, my opinion might be different, but the situation would be quite different as well.

If, despite his current stated intentions, he ends up having little or no presence in this child's life, trying to explain how her child got his/her last name might be a burden for Ashley, and a source of resentment in the future. If the child and father remain close, the child can choose to adopt the father's last name later, I know of a girl who did the opposite, after her parents went through a horrific, accusatory and bitter divorce, she took her mother's maiden name as her last name, and her mother reverted to her maiden name as well.

The baby having a different last name than its mom causes unfortunate questions and confusion which some people are now used to, but others are not.