Mother’s middle name on child birth certificate not listed?

I just had a baby boy and I am waiting for his birth certificate to get his passport.
But I am scared that my name on his BC and the one on my passport won’t match. My entire name is Mary (first name) Joseph (middle name, dad’s name) DuPont (last name), Mary Joseph Dupont.
So on my son’s BC I only wrote Mary DuPont and I will use my passport, in which my full name is used, to retrieve his passport. Every other information regarding me on his BC is the same as in the passport. Can the passport agency refuse to give me his passport because my name is incomplete on the birth certificate? Will they ask or an amendment because of my middle name missing?
PS: i am the sole guardian of my child