DHS and SSA should ask employers to post a sign in theirs office that states that the names on their SS card should be the same as the names they put on the form I-9. When jobs hunters fill out their form I-9 for employment, this would save time for both parties and avoid letters bean sent to either parties about mismatch names.
Since the Social Security Administration records (i.e. Social Security Number) is a part of the eVerify system, I suggest that the "expiration" line on List C be used to enter the name as it is on the SSCard. This will encourage employers to enter employees under the name on record with SSA. This will also reduce the number of no match letters that are issued to payroll departments.
Not sure if I am the only one, but I process E-Verifies for multiple companies. I have to be on my toes in order to guarantee that I have logged onto the correct companies account. If E-Verify could list the companies name any where on the website it would help significantly.