I tired to register my younger S who is a high school freshman for a dual credit course at a CC and also open a minor savings account at a credit union recently. Both came back with an "SS# Does not match name" response and the credit union is refusing to open the account unless I get a letter from the SSA that SS# on their records matches my son's name. What they tell me is that someone else (with a different name) has been using my son's SS number for several years. We never have had to use his SS number for anything before. Anybody has any experience on how to deal with this or how to approach the SSA.
I'd go to SSA & bring your son's original SS card, birth certificate & any other ID he has and make an appointment to talk with someone there. Do NOT have personal experience with this issue but imagine it is not as uncommon as we might think.