J.Y.
You may want to consider adoption. With name change, if something happened to you, and your ex was legally next of kin, your daughter could find herself living with someone she does not know. The good news, adoption fees are 100% reimbursed on your taxes up to $10k. Believe me, as I have been through this, it is worth it to have the peace of mind that your daughter belongs to you and your husband and no one can come and mess it up.