That's an interesting question. My son is 2 and I highly doubt he knows my name. Like he's heard it tons of times but I doubt he knows that it's referring to me. Especially bc he just knows me as mama.
I know I learned my mom's nickname early on cause my step dad kept calling her by it, and I went to say it and she cut me the evil eye telling me I wasn't allowed to call her that.
My older sister used to call my parents by their names because that's what they called each other, so after that they started calling each other "Mama" and "Daddy" so she would stop calling them by their names