Birth certificate question!

My son is 9 months and I always wanted to add a middle name but when I was in the hospital my parents practically forced me to just do one. I felt like a 10 year old not being able to make a decision of my own almost being 30. Thing is I want to add a middle name it was meant to be in his birth certificate. But I am worried I won't be able to since I already got him his passport at 2 months because we travel a lot.

Is there any way I can still add it?

Someone please help me with this?

Google is not being helpful at all!