Im 20 years old and want my dad's name on my birth certificate

You can't add a name on the birth certificate. Your father, however, can have your birth certificate amended if he is proven to be your legal father, either through paternity acknowledgment or genetic testing.

Forgot to add this: There may be a limit on the time your father has to pursue this action, and this will vary based on your location. Your local office of vital statistics or department of health and human services can offer more details on the process.