My son was born in NJ, his fater's name is not in his birth certificate, now I am married to his fater and we want to change his name, how can we do that?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

If the Father's name was not on the because, you will need a court order to add his name. This may also require a paternity test.

First its not a good idea to piggyback your question on someone elses. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

if the Father's name was not on the b/c, you will need a court order to add his name. This may also require a paternity test.

Do I need to go to NJ to do that

You should be able to do this in your state, if all you want is a simple name change,

If you want to get father actually added to birth certificate, then yes you will have to file in the state where the birth certificate is issued.