My father's name is'nt on my birth certificate. Wondering how much would it cost for his name to be added to my birth certificate, and how much would it be me to change my last name to his.

See a lawyer. Such costs can vary widely.

In my area, it doesn't cost anything to change your last name (I just did it), just the proper legal documents. I'm not sure if its even possible to add a parent to an existing birth certificate.

You have a unique situation and you'll need to consult a lawyer for help.