I am legally married, my husband moved out about 3 yrs, I have a boyfriend and we just had a baby and the hospital did not allowed me to put my boyfriends name on the certificate. How can I add my boyfriends name to the certificate

If you are still married (you didn't say divorced just that husband moved) then he is the presumed father legally. If you know that your boyfriend is the father then he petitions the court for a DNA test to prove he is the father. A birth certificate is a legal document and therefore needs a court order to be changed. The DNA test will need to be done at the court approved facility.

Also, any question on law needs to include your general locale because local laws vary to some degree.