Earlier quoted context omitted.
This is true (in my experience) for search results but not for the chrome web store. Sure, you could take Google to court if you have more money and time to waste...
Searching turns up https://adampash.kinja.com/google-just-dmcaed-my-chrome-exte... , which has the text of an email Google sent out that does include the sender information. You can submit a counter-notice, and if for some reason they didn't give you the required information I'd expect you could contact support and ask for it.
You'll note how in that example, they provide lots of information on the party that filed the DMCA claim. That info is only provided to you if the DMCA notice actually included the info - Google will for some reason process malformed notices that don't contain the required information, which leaves you with no options.
In this case the person filing the claim provided no information except their name (4 japanese kanji) with no further contact information or other details. I was unable to find them on Google, if that was even their name.