How do I legally add a suffix to my son's name?

My son is 3 years old and yes I know, why didn't I add it sooner.. Well, I didn't think about it until recently since he will be starting school soon. It's confusing when we get mail or when I had to fill out paperwork. I live in CA, and I was wondering how do I legally add the suffix II to his name? For example, his father's name is Nathaniel Brandon Creek, my son's name is Nathaniel Kole Mason Creek. What steps would I need to take to get his name from ^^ to Nathaniel Kole Mason Creek II ?