My husband wants to adopt my first born there is no name on the birth certifacate is there a way to put his name on it now??

If you do, you're creating a lie for your child.

Honestly, I don't really think it's legal to just "put" someone's name on a birth certificate.

See a family lawyer about starting the adoption process.

Is your husband the biological father of the child?
If so there may be a way to prove paternity and add his name?
If not he needs to adopt the child.