Do I have to divulge finances and employer in a modification/contempt case?

In such a proceeding, anything you wish for the Court to know the other party is entitled to know as well. Jack Berner DISCLAIMER: This answer is provided for general educational purposes only. By using or participating in this site you agree and understand that there is no attorney client relationship between you and the attorney responding, and no attorney-client confidentiality. The law changes frequently, and varies from jurisdiction to jurisdiction. The information provided in this answer is general in nature and may not apply to the factual circumstances described in your question. The applicable law and the appropriate answer may be different in the State or States where the relevant facts occurred. For a definitive answer you should seek legal advice from an attorney who (1) is licensed to practice in the state which has jurisdiction; (2) has experience in the area of law you are asking about, and (3) has been retained as your attorney for representation or consultation. Your question and the attorney’s answer may be used for promotional or educational purposes.

There is probably no way around it.

There is no requirement that you file a financial declaration unless there are financial issues before the court. Howver, in a modification case, there are often also issues related to child support. In that situation, your income would be relevant and you would be required to disclose it. If there are safety reasons why the name of your employer should not be disclosed, you should consult an attorney to discuss how you can protect yourself.