The general allegations, and the argument in favor of pseudonymity, are here; the argument against pseudonymity is here. Magistrate Judge Andrew Baxter (N.D.N.Y.) didn't release a written opinion, but stated that the motion was denied "for the reasons stated on the record during the stenographically-recorded telephone conference on 5/24/2023"; I expect no transcript has yet been prepared, but if the plaintiff appeals to the District Judge, the transcript will likely be filed at that point.
To my knowledge, plaintiffs alleging that they had been raped or otherwise sexually assaulted are more often than not allowed to proceed pseudonymously in federal court, but there is a large minority of cases in which such motions are denied; see PDF pp. 78-85 of The Law of Pseudonymous Litigation. (My sense is that there's also a split among state court cases, but I can't speak to that with confidence.) Here's an excerpt from Rapp v. Fowler (S.D.N.Y.), in which pseudonymity was likewise denied; Fowler is Kevin Spacey:
[1.] The harm that C.D. claims would result from the public disclosure of his name would be the "re-trigger[ing]" of his post-traumatic stress disorder ("PTSD"), which he allegedly developed as a consequence of the assault…. [But] even assuming there were no "leak" of C.D.'s identity as the case proceeded, "[b]eing 're-exposed' to the perceived wrong [of which he complains] is an inevitable consequence of litigation itself. If the case goes forward, [plaintiff] will be deposed, no doubt in the presence of the accused defendant; in the less certain event of trial, [ ]he will presumably testify in a public courtroom and be subjected to cross-examination." Neither of the declarations suggests that proceeding with the case anonymously would protect C.D. from those consequences.
[2.] [Pseudonymity is not justified here] despite the harassing Instagram comments that Rapp received after he went public with his allegations against Spacey, which C.D. implies that he will receive if he discloses his name…. [W]hile online harassment of any kind is repugnant, it is an unfortunate consequence of the social media age. Many who make accusations against public figures are forced to endure it. Without a specific threat of harm and a privacy interest that outweighs the prejudice to the defendant and the public's right to open courts, however, C.D.'s allegation that he would be subjected to online harassment if he were identified, even if it proved accurate, would not alone entitle him to proceed by anonymously.
[3.] Spacey has shown that he would be prejudiced during discovery because C.D.'s use of a pseudonym likely would prevent persons with information about C.D. or his allegations that would be helpful to Spacey's defense, but that now are unknown to Spacey, from coming forward.
