Need Answers Very Important

So when my son was born and we finally got to go home i noticed on the mothers copy of the birth certificate that they give you at the hospotal that my son's nane was spelled incorrectly so i called vital records to get it corrected but when i went to get his social security card they said the incorrect name was the one that was in their system so i ended up calling vital records to see had they changed it and they did .i went to get his birth certificate and his name was spelled correctly but how do i get it fixed on his ss card ?