Birth certificate

Lindsey

Ok so please no judgement!!! I am currently pregnant by the man I am currently with and we have been together a year on the 22nd of this month. Well I am also legally married but I have not seen my legal husband in over 3 years we have both moved on with our lives just haven’t divorced. What happens when the baby is born will they let me give our child the fathers name and let me put him as the father?