The first question is, would you have any basis for legal action against a service provider in case they arbitrarily delete your contributions: you might, or you might not (read the terms of service, ask your lawyer). Let's assume that there is a legal reason why the provider should leave your material alone. If you are infringing copyright, the provider might also get sued for contributing to the infringement, so there is a law DMCA: 17 USC 512) that says when they are immune to such a suit. The first part of this is that a supposed copyright owner can file a take down notice with the provider, claiming that they are hosting infringing material. But under thatlaw, they must "take[] reasonable steps promptly to notify the subscriber that it has removed or disabled access to the material". Presumably they did that and inform you about the counter-notice provision (although your wording is not clear on this: saying verbatim what they notified you of would be useful).
That counter-notice requires you to identify yourself, etc. and provide
A statement under penalty of perjury that the subscriber 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.
There is no point in the law requiring the provider to reveal anything about the alleged rights-holder, just the fact that the material has been taken down. The law does allow the copyright owner to subpoena requesting information identifying the alleged infringer. There is no provision whereby an alleged infringer can subpoena information about the person filing the original notice. That is because the copyright owner has to file a lawsuit against the infringer (if the infringer files a counter-notice and the owner does not file lawsuit, the material must be restored). When you get sued, you will know at that point who is suing you.
You do not need to know who the rights holder is to file a counter-notice. The law says that you have to include
A statement under penalty of perjury that the subscriber 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.
Suppose for example that you illegally copied and pasted the source code for Windows 10. You can't seriously believe that you have the right to post that material, so to avoid perjury charges, you would not make such a false statement. Suppose that you copied two lines of protected source code, as examples of some technical point – then that would be fair use and not infringement. In such a case, the initial take down notice might be found to be abusive and knowingly false. There could be an intermediate situation, where you post a book that you've written and as it happens there is a graphic contained therein which is beyond the scope of fair use – but you have no idea that this is what they are talking about (maybe you think the graphic is not protected). Then perhaps you can, in good faith, state that the claim "this work infringes" is mistaken. This is where you need to talk to a lawyer, to see if you can in good faith deny infringement.
As the law currently stands, there is little burden of proof on the person filing the take down notice, until the matter is argued in court.
