So in the US, at least, if you're going to sue someone over IP violations, you should plan on your identity being made part of the public record. As a country we're pretty adamant about that. It's a feature, not a bug.
I'm including DMCA notices in things I believe should be -- must be -- transparent. They're legal filings after all, strongly implying that if you don't comply, you're about to be sued. Your proposal would allow, say, Oracle to hide their identity if they were filing a complaint against the Linux kernel so that they could get the benefit of launching a legal salvo without the reputation hit for having done so. I believe that's far more unfair, and more likely, than your scenario.