Maybe you’re describing YouTube’s DMCA process? The actual law doesn’t specify any of that [1]:
> If the user believes that the material was removed as a result of mistake or misidentification of the material, the user may submit a counter-notice requesting the reinstatement of the material. To be effective, a counter-notice must contain substantially the following information:
> (i) a physical or electronic signature of the user;
> (ii) identification of the material that has been removed or to which access has been disabled and the location at which the material appeared before it was removed or access to it was disabled;
> (iii) a statement under penalty of perjury that the user has a good faith belief that the material was removed or disabled as a result of mistake or misidentification of the material to be removed or disabled;
> (iv) the user’s name, address, and telephone number, and a statement that the subscriber consents to the jurisdiction of Federal District Court for the judicial district in which the address is located, or if the subscriber’s address is outside of the United States, for any judicial district in which the service provider may be found, and that the subscriber will accept service of process from the person who provided notification under subsection (c)(1)(C) or an agent of such person.
(iv) sure sounds like giving them your true identity to me.
You have to give them information to sue you (or do other nefarious things), but they don't have to provide you with information that say, you could use to sue them for perjury or try to recover damages from the time it was taken down.
Again, you seem to be conflating YouTube’s DMCA process (which is designed to optimize the experience for YouTube, not to maximize the rights of YouTubers) with what the law actually specifies. The filer must provide contact information (paragraph iv), which can be used to serve process.
> (i) the signature of the copyright owner or an authorized agent;
> (ii) identification of the copyrighted work claimed to have been infringed, or, if multiple works are on a single site, a representative list of such works;
> (iii) identification of the infringing material or activity (or the reference or link to such material) and information reasonably sufficient to permit the OSP to locate the material (or the reference or link);
> (iv) contact information for the copyright owner or authorized agent;
> (v) a statement that the person sending the notice has a good faith belief that use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law; and
> (vi) a statement that the information in the notice is accurate, and under penalty of perjury, that the person sending the notice is authorized to act on behalf of the copyright owner .
I agree the system is intentionally asymmetric, because it was built by people who understand how quickly material proliferates once it’s been posted to the Internet. That makes it abusable to chill speech, as in this case. But the law was also written with an expectation that anonymity does not guarantee full participation in civil society.
> If the user believes that the material was removed as a result of mistake or misidentification of the material, the user may submit a counter-notice requesting the reinstatement of the material. To be effective, a counter-notice must contain substantially the following information:
> (i) a physical or electronic signature of the user;
> (ii) identification of the material that has been removed or to which access has been disabled and the location at which the material appeared before it was removed or access to it was disabled;
> (iii) a statement under penalty of perjury that the user has a good faith belief that the material was removed or disabled as a result of mistake or misidentification of the material to be removed or disabled;
> (iv) the user’s name, address, and telephone number, and a statement that the subscriber consents to the jurisdiction of Federal District Court for the judicial district in which the address is located, or if the subscriber’s address is outside of the United States, for any judicial district in which the service provider may be found, and that the subscriber will accept service of process from the person who provided notification under subsection (c)(1)(C) or an agent of such person.
1: https://www.copyright.gov/512/