Yes, you can name the baby on the original birth certificate. The adoptive family will also enter a name on a new birth certificate when the adoption is finalized. You will need to discuss your feelings about keeping the name you choose with the adoptive family because naming the baby is a very important issue. Some adoptive families have a special name that they have picked out for many years to name the child. Many adoptive families are more than willing to either keep the name you choose or work together with you to choose a name that you both like.