In every proceeding or action brought under this act, the anonymity of any woman upon whom an abortion is performed or induced or attempted to be performed or induced shall be preserved from public disclosure unless she gives her consent to such disclosure. The court, upon motion or sua sponte, shall issue orders to the parties, witnesses, and counsel and shall direct the sealing of the record and exclusion of individuals from courtrooms or hearing rooms to the extent necessary to safeguard her identity from public disclosure. In the absence of written consent of the woman upon whom an abortion has been performed or induced or has been attempted to be performed or induced, anyone who brings an action under Section 3 of this act shall do so under a pseudonym.