Generally speaking, plaintiffs who want to use the civil justice system must sue in their own names, even when that might damage their reputations and professional prospects. Someone suing an ex-employer, for instance, may worry that future employers might not want to hire a known litigious employee; or he may expect that the employer will argue that he was fired for sexual harassment, theft, incompetence, etc., allegations that will then be connected with his name (even as he argues that they are false and that the real reason for firing was, say, race discrimination). Likewise, a libel plaintiff may worry that the lawsuit will just further amplify the libelous allegations. But that usually doesn't suffice for pseudonymity, unless the plaintiff can show a serious (more than merely speculative) risk of physical harm stemming from being identified, or the case involves a purely legal rather than a factual challenge.
But when the case involves controversial topics that might arouse public disapproval, cases are split. For instance, a recent case rejected pseudonymity where plaintiff argued that his challenge to Twitter policies might draw attacks on his children from "unbalanced people in the world" who "hate President Trump supporters." Another rejected pseudonymity for plaintiffs objecting to a school's "Black Live Matter" posters. But other cases allowed pseudonymity for challenges to school board policies on teaching views associated with Critical Race Theory, or on gender identity. And cases are split as to whether challenges to vaccine mandates may proceed pseudonymously.
Now let's throw in another factor: What if the case is a challenge to a university disciplinary proceeding? When it comes to challenges to sexual misconduct findings under Title IX, most courts have allowed pseudonymity (see Appendices 4a & 4b of The Law of Pseudonymous Litigation), though the Seventh Circuit has just strongly disagreed with that majority view. Should pseudonymity be more broadly allowed in all university disciplinary proceedings, whether or not they involve sexual misconduct?