You should inform your employer of the correct information and ask them to issue a corrected W-2. The name is less important than the SSN. A mismatched SSN should always result in an inquiry from the IRS and will probably delay your refund substantially, and may require you to go to a local IRS office with proof of your identity. A SSN mis-match will also mean that your wages are not going to your credit at the social security administration so you won't be getting appropriate credit in case of retirement or disability.
