From Judge Ronald A Guzmán's decision in Doe v. Sandler(N.D. Ill. 2011), which I just came across—as I read it, the judge began the case being open not just to pseudonymity but to sealing (the original TRO, for instance, is sealed, which is very rarely done for court orders), but ultimately seemed to sour on that:
Plaintiff, Jane Doe, has filed a Verified Complaint asserting a claim for invasion of privacy based on public disclosure of private facts under Illinois law.
In summary, plaintiff, a self-described married woman, civic and church leader, became embroiled in an affair. During the course of the affair she and her partner made photographic and video recordings of an intimate sexual nature. These recordings subsequently fell into the hands of her sexual partner's "girlfriend" who has threatened to publish the video and photographic evidence of their sexual conduct in different ways, including through the Internet for all the world to see, expose her behavior to her friends and social and religious groups, and has even attempted to extort money from plaintiff, her husband and the parties' mutual sexual partner—whose identity plaintiff also seeks to protect by using the pseudonym "Richard Roe."
On February 25, 2011, the Court granted an ex parte temporary restraining order prohibiting the defendant from distributing or causing to be distributed any photographs or video of the plaintiff in the defendant's possession. {The Court denied plaintiff's request to restrain defendant from communicating knowledge of plaintiff's conduct to others.} At that time, the Court advised plaintiff's counsel that in considering any subsequent motion for a preliminary injunction, the issue of the appropriateness of the defendant's continued use of a pseudonym, "Jane Doe," in place of her real name as well as the issue of keeping filings under seal would have to be more fully addressed.
Subsequently, plaintiff's counsel moved for entry of a consent decree to be filed under seal. The proposed consent decree purports to be signed by the defendant, though the defendant has never appeared, by counsel or otherwise, and there is no indication in the record that she has been at any point in time represented by counsel in any capacity.