My question involves name change laws in the State of:

I WILL APPLY FOR CITIZENSHIP BY NATURALIZATION SOON, BUT MY 15 YEARS SON'S SURNAME CHANGED IN HIS BIRTH CERTIFICATE. HIS BIOLOGICAL PARENTS FILE A COURT CLAIM IN MY COUNTRY TO PUT HIS SURNAME INSTEAD. NOW WITH THIS CHANGE, MY SON'S GREEN CARD AND BIRTH CERTIFICATE HAVE DIFFERENT LAST NAME. CAN I CHANGE HIS SURNAME DURING NATURALIZATION PROCESS?