You CAN just change your son’s surname. Just start calling him by yours. Tell his school, doctor, anywhere he uses a surname, just tell them it’s changed. I was known from birth by a different surname than the one on my birth certificate, never caused us any problems. Only if he wants to get a passport will he possibly have to use his father’s surname, though if he can show school reports and doctor’s records in your surname that might not even be a problem. I’m 50 and still using the “adopted” surname, and it causes me no problems; I even have a passport in this name.