change last name in birth certificate

My son is using a totally different name. He is using my maiden name. I was under the impression that my ex did not file his name in the civil registry. I filed a new one and when I requested an nso birth certificate, that's the only time I found out that my ex had filed a birth cert for my son using his last name. My son has been using a totally different name since I was under the impression that the birth cert I submitted is correct. The question is, how can I have the previous one deleted or nulled since my son has been using my last name for 8 years now. This is what he use in school and other documents. I am having problems getting an nso birth certificate because they are saying that there's a duplicate. Second question is, I would like my son to use my legal husband's lastname since I am now married. What it the process for that?

do you mean that the first birth certificate does not have your signature?

the lasting solution is for both you and your husband to adopt him.

It has my signature but I was under the impression that my ex did not file it since we parted ways.

The first thing I want to resolve is for my son to have a vaid nso birth cert with the name he is using now which is my maiden name. Is there a process that can be done in order to have the first one removed? There's this thing I heard abou having it annotated. I just don't know what that means

Basicall all i wanted first is for him to have a valid nso birth cert using his current name. How is that possible?

imo, the first birth certificate is valid; the second one is not. again adoption is the best solution.