My dad died when I was 3 and my mom never put him on the birth certificate. She left me when I was 9 and lives in Samoa but she doesn't want to contact me. Is there anyway I can put my dads name on the birth certificate because my grandma is trying to take me to the doctors but they won't let her because my dads name is not on the birth certificate. She's trying to get Survivors Benefit for me too.

I am 14 and my grandma is from my dads side.

... but they wont let her because my dads name is not on the birth certificate. ...

There are other ways to prove that he was your father. Changing the BC is not necessary.

If your grandmother really wants to change your BC, she should contact the vital statistics office in the state or country in which you were born. Rules vary from jurisdiction to jurisdiction.