Hi there is no father named on my daughters birth certifcate how can I go about add my partner to it

There are two ways for unmarried parents to establish paternity :

1 Signing a voluntary form called an Acknowledgment of Paternity (available from hospitals, local district child support offices, and local birth registrars); and
2 Filing a court petition to have the court determine paternity.

BTW if he is not the biological father , he will have to adopt her.

Agree, it sounds like your partner is not the child's real bio father. So your partner will have to adopt the child. Which will require the bio fathers permission normally.

Just because he is not listed on the birth certificate, it does not mean that the bio father does not have legal rights