I agree with Mr. Whitaker. Also, the attached link may be helpful to you.
Please do not consider this answer legal advice. My answer is for informational purposes only. You should contact your attorney to obtain advice with respect to any particular issue or problem. The answer does not create an attorney-client relationship or privilege.
John W is correct. Counsel can negotiate a deal for you, and only at the end, when it is time for a release to be drawn, is it necessary to reveal your identity as the person being released.
Licensed in Maryland with offices in Maryland and Oregon. Information here is general, does not create a lawyer-client relationship, and is not a substitute for consulting with an experienced attorney on the specifics of your situation.
Frankly, you can't. Which is why people named as "John Does" hire my firm to negotiate settlements with these types of companies.
Unless the cable company will serve as a middleman you need a representative to write Copyright Infringement, LLC if you want to settle and remain anonymous. That needs to be done by someone who knows the legal ramifications of each word used in writing them. That means an attorney.
Most settlers take the gamble, write direct, and rely on Copyright Infringement, LLC not to welch on the deal. I am not aware of any reported incidents of them welching by raising the settlement figure once they give it. If anyone has, let us know.
So far, this is free to you. Until you pay a fee, I am not your lawyer and you are not my client, so you take any free advice at your sole risk. I am licensed in IL, MO, TX and am a Reg. Pat. Atty. so advice in any other jurisdiction is general advice and should be confirmed with an attorney licensed in that jurisdiction.