Yes, you may choose to name your baby and that name will appear on the original birth certificate. However, the adoptive family may choose to change that name. Many times they already have names chosen or they may choose to use the name you have selected as the child’s middle name. Please be sure to get a copy of the birth certificate for yourself if this is important to you. After the adoption, the baby’s birth certificate will be changed and you will not be able to get a copy of the original with the name you selected.