Try Wikipedia then, or search through some tech sites.
It doesn't. If that's all you'll ever do with it. But what happens if you lose your MP3 player?
Ofcourse there are people who don't mind having their names attached to stuff. I'm just not one of them.
Let me give you another example where you leave traces without noticing it: if you install (for those who use M$ software) Word it will automatically save your credentials (the name you used to install the program or Windows with), date, editing time, etc. to any document you created. If you archive that document or distribute it later by any means people can still trace it back to you. If you're okay with that, than that's fine. I realize this isn't an example of DRM, but it's still a privacy issue in general.