Name change after birth?

My baby boy was already officially named ... we each had a first name we liked and could not agree so we picked the name at random from the two names and my preferred name was chosen. He chose the middle name and baby will have my husbands last name (different from mine). Now he is asking to change the middle name to something that I don’t care for. We would have to change it on the birth certificate because the information has already been submitted.