What is a Name Change document? If name has not changed, can birth certificate suffice?

Hey, Joan! You know, the initial "R" can stand for Robert, Ross, Robin, etc., you can't tell whether this "R" here just refers to "Robert", so it is normal that the embassy has doubt on this. The Name Change document can be a letter from local authorties proving that both names are yours. You can ask the organization which issues you the current passport to provide this letter.