Earlier quoted context omitted.
You can't pseudonymously contribute to most OSes of note. Linux for example.
I'd just like to interject for moment. What you're refering to as Linux, is in fact, GNU/Linux, or as I've recently taken to calling it, GNU plus Linux. Linux is not an operating system unto itself, but sure you can contribute to the Linux kernel pseudonymously. Think of a plausible name, "git commit --signoff", and you're good to go. There's no enforcement of slave names for kernel contributions, it's all just a min…
You can lie about your name, I suppose, but strictly speaking you're violating the stated rules and could face having your code rejected or removed: "code from anonymous (or pseudonymous) contributors will not be accepted". (https://www.kernel.org/doc/html/latest/process/1.Intro.html)
And since you mentioned GNU, would you be able to pull the same trick on a GNU project? Don't they require you to sign away your copyright, with paperwork? So you wouldn't be able to contribute to (some portions of) GNU/Linux pseudonymously.