I am not licensed in New York. I provide my answer based on handling hundreds of these cases over the last eight years.
You should speak to an attorney about this matter. There are a number of options to consider. You can wait to see whether they obtain your identity and if they file a lawsuit against you. However, this could result in increased settlement demands and your name unnecessarily being included in the litigation. On the other hand, you may never be sued. I usually caution against what I call the "wait and see" approach.
Alternatively, you could file what is called a motion to quash or a motion to set aside a subpoena seeking to preclude disclosure of your identity. You could spend more in doing so than you would in a settlement. Moreover, you could file the motion only to have the plaintiff dismiss the case and refile correcting some of the issues raised. The Court could deny your motion and you would be in the same place with a possibly higher settlement demand. Even if the court granted the motion, the plaintiff could refile the litigation assuming only procedural issues caused the dismissal.
Depending on circumstances, you could also file a motion to dismiss for lack of personal jurisdiction if you live in one state and the litigation is pending in another state with which you have no or minimum contacts. But again, even if you succeed, the plaintiff could refile the litigation.
Finally, you could try a third approach and make efforts to settle the matter. The terms of the agreements are confidential. As such, I cannot discuss amounts or specific terms. However, this would resolve this litigation.
You really should consult an attorney who has absolutely practiced in this specific arena and have them answer most if not all of your questions. You should not need to pay for an initial consultation.
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Yes. This is the preliminary step to bringing a civil action against you for copyright infringement. Without knowing whether its for music, movies, pictures, or other media, I can't really give you much information, but you should definitely seek local counsel with IP experience for a consultaiton. I'd be glad to talk to you if you'd like. You can email me at firstname.lastname@example.org or call my office 212 448 9933