My illegal husband works under a different name, so how would I go about that when talking to the lawyer to start the legal process?

Your hmyour husband needs to fully disclose this information to an attorney. He also must discuss why he has used a different name as well as whether he also used a social security number issued to another person. It would also be important to know whether your husband ever completed any I-9s or other documentation that required his immigration status to be disclosed.