Name change for baby?

When our sweet little boy was born, we had already decided on his name. Noah Arlen Martin. Two weeks after he was born, my grandfather passed and I decided that I wanted to add a name to represent him. Noah J. Arlen Martin. But I had already written out his name as it legally is on the birth certificate. I know that a last name change is more common, but does anyone know how I’d go about legally changing his name?

Also, here’s a picture of the cutie. ❤️