Change Gamecenter account name not username

When i was little my mother set up my itunes account as her name. Well that was over 8 years ago and now i want to change my account name. I went to itunes and changed it to my name but on gamecenter whenever i want to add a friend it still says "[my moms name] would like to be your friend" so what im asking is how do i say so it says '[my name] would like to be your friend automatically so i dont have to keep changing it. And i synced my iphone and computer after i changed my itunes accounting info.