My Name On My Ss Card Is Different From My Birth Certificate. What Should I Do?

It really depends on which state or local authority you belong to. Depending on the state, you can usually amend the birth certificate based on the fact that the name is not correct, and you've been using a different name your whole life.
If you have evidence, or the correct sort of documentation that clearly shows the name you've been using, (i.e. Your social security card, driving licence or passport), this should be sufficient enough for the state to amend your birth record accordingly.
You can also get in touch with the Vital Statistics office in the state where you were born. You can also try the city hall that may be able to assist with these types of things.
There is an alternative way where you can submit three documents; a marriage license, one copy of the child's birth certificate and a school transcript, and provide the name that you wish to use from now on.
All you have to do now is wait for the mail which should be no more than a few weeks. In fact, it costs less than five dollars for the entire process and once completed a certified copy of your corrected birth certificate is sent.

First, ensure your legal name matches your birth name (you may need to have your name legally changed to match if it doesn't already).  Once your name legally matches your birth name, you can have it changed on your SSN/card by going to the SSA website for the appropriate form, where you will also find step by step instructions.   Then you take or mail the completed form along with "proof" documents.  In the case of name change,  you must show them a recently issued document to prove a legal name change including:  Marriage document,  divorce decree, certificate of naturalization showing a new name; or court order for a name change.

If the document you provide as evidence of a legal name change does not give them enough information to identify you in our records or if you legally changed your name more than two years ago, you must provide Social Security with additional documentation.  Here is the website address to go to for detailed info:  
ssa-custhelp.ssa.gov

My father is having the same problem His name on his birth certificate and birthday is different from what is on his SOS card and DL. I don't understand how he got a SOS and DL card in different name then what is on birth certificate. Not sure how to change his birth certificate to match his name he has used all his life.

Call the social security administration, they can help you change the name on your social security card.

In the same boat. Except I have no proof that my social security name was once my legal name because ive never used it and it never existed...except on my card. Which screws me over of ever driving. Trying to find answer......

My friend had the same problem before. All he had to do was file for a legal name change. You can get the legal forms you need to file for a legal name change in your state at [ LegalFormsBank.biz ].