My spouse first came to the US on J-1 visa. She returned to her home country for 3 years and now is back in the US on H4 visa. We married during the 3 year period she was at home country. She has a SSN but her last name has changed now. She went to SSA office and they told her that they could not update her social security card/record because she is not eligible to work. However we are filing taxes now (married jointly) and our application was rejected because her name and SSN mismatch.

Does she need to file W-7 also, or the answer she got at the SSA office that they could not update her name was incompetent?

Thanks in advance.

Resubmit the return using her old name. Done all the time.