My concern is that I haven't previously established his U.S. citizenship before, what documents or paperwork do I need to do this?
We will need to see proof of U.S. citizenship.  Just so that you know, we can only accept certain documents.
Ok. I want to change his name on his Social Security card, do I need certain documents for that?
Yes, you will need to show us proof of his legal name change or final adoption decree.