Social Security Issues: My Father Can't Renew Drivers License Because Name Does Not Match Birth Cert

My father was born in 1953 and given the name L C P , born on a naval base hospital, his mother and his biological father divorced soon after which she remarried. My fathers SS Card was issued when he started school, without showing a birth certificate, and my grandmother used the name M T P, to register him for school, so that's what his ss card says, he went by that name and also by his stepfathers surname C***nell, but his drivers license and ss card were issued M T P. I think my grandmother had planned to legally change his name to M T P but it was never legally changed. How can we get his ss card name corrected to L C P, his legal name, without changing his name to the erroneous name M T P. He does not work we live on my disability, and barely scrape by, name change in my county is expensive, I don't think he should pay for the ssa giving him a ss card in the wrong name because it issued without showing birth certificate. Thank you for any help

Social Security Issues: My Father Can't Renew Drivers License Because Name Does Not Match Birth Cert