The penguin's name is "Tux" and he's the official Linux mascot.
I think Linus Torvalds picked it a long time ago, he said he wanted something that was non-threatening, so hence the penguin lol.
The debate about Linux vs GNU/Linux imo, is one of the stupidest and pedantic debates I've ever heard. Maybe it mattered 30+ years ago when things were much less developed and only hardcore nerds and programmers used it, but now days it's only important to grognards and neckbeards.
Hot take, but it's like those pretentious music enthusiasts that will argue about what precise genre an artist fits into. "I would say they are post-progressive indie skitzo-pop. No way! They are clearly more neo-grunge sca-punk with post-rock elements" who cares?? Have your ultra-precise categories in your personal music collection all you want, but acting like it's based on some hardcore objective truths of the universe is stupid.
Nobody is confused when I say I run Linux as my OS. Actually, people do get confused but it's not because of GNU/Linux, it's because they haven't ever heard of Linux and thought that Windows and MacOS were the only 2 OSes for computers.
If somebody genuinely pulled an "um, actually" on me for saying Linux vs GNU/Linux, I would scream laugh loudly and then change the subject.