Should an ITIN client report his W2 that does not match his name?

Hello out there,

Interesting scenario which I have not encountered and not sure how to go about it. I called IRS and that found myself being disconnected several times and or get the message they are busy. So I turn to you all for suggestions. ITIN client comes in, has been working for Company X, with, not a surprise, a social that is not his. Of course normally we still file taxes which the name on the W2 matches the ITIN taxpayer and the system understands which asks we provide the social that is noted on the W2.

The difference here is that the client name on the W2 does not match the ITIN filer. He mentioned he has worked this social under THAT name for years. He wants to file taxes, but gets different input from different preparers which scared him to not reporting it as its illegal to file a W2 that his name does not appear on it. He is the person working the income and filed only two years but now is not sure if he should or not continue filing. Again, tried calling IRS for guidance and have not been able to get through. Any suggestions; how you would handle this case?

Input greatly appreciated like always.