It will be easy changing your child's surname from yours to his. The procedure is called Legitimation by Subsequent Marriage.
Better if you can have him sign the acknowledgment in the BC. It becomes additional evidence of his paternity.
Yes you can still have your baby use your surname even if he signs the acknowledgment of paternity in the BC. So long as
For legitimation, you have to submit documents to the Local Civil Registry where your child's birth is registered. The documents include the CENOMAR, marriage certificate, birth certificate of the child, IDs of the parents, and a joint afffidavit of legitimation signed by yourself and your baby's father. An interview will also be conducted by the LCRO before your baby's records are sent to the NSO for annotation.