I am having very nearly this same issue and would dearly love an answer. The other respondent is correct, in the state of Georgia, a married woman MUST list her husband's name on the birth certificate. In fact the forms you fill out don't allow you not to, so you were not falsifying information. Georgia law has a "presumed" parentage stance when it comes to fathers. If you are married at the time of the child's birth (regardless of whether you are separated), the legal husband is the presumed father and therefore is responsible for the child unless he or the biological father files a court order disputing parentage. And even then, it is possible for the courts to rule that the presumed parentage stands if the dispute is not filed within a timely manner after the child is born (i.e. if too many years have passed).
I know all this, but I still don't know how to do what I need to do. My husband and I were separated for 12 years, but didn't get divorced until three years ago (we didn't want the paperwork and hassle, and were fine living our own lives). During that time, I gave birth to my son, whose father I have been with for the past 10 years (and because of whom, in fact, the divorce came about...can't get remarried without first getting divorced)! It was only just recently that I realized the birth certificate for my son has my ex-husband's name and not his biological father's name (soon to also be his legal father by way of marriage). We want to change this, but do not want to go to court. My ex and I both hated the divorce proceedings and would rather just do this quietly, quickly and efficiently. My fiance is willing to submit to a blood test and my ex is willing to write a statement indicating our lack of involvement for the past 13 years or so. Will we HAVE to go to court? And if so, will my ex have to attend? He's not even in this state anymore!
Any assistance would be appreciated!