I don’t use “google search” because it is nonfree software; linux was not started by the GNU project members. However, GNU does have a linux, it’s called Linux-libre.
GNU is the operating system in its entirety. GNU/Linux is the name used to best describe the exact operating system by giving principal credit to the Linux foundation. The GNU part is to highlight the fact that it is a libre operating system first and foremost.
Perhaps I need to reread the essays again, but the main takeaway is that what’s at stake here isn’t credit but the political legacy of software freedom. Something that is made obvious by your last remark.