When you submit a documentation PR to an open-source project, do you put your name (real, screen or otherwise) in the section of documentation that you add? No; you let Git put it in the commit history. (And if you have to discuss it, you put it in the discussion, or let a forum system such as GitHub's put it there for you.)

Stack Overflow is the actual document being worked on, not the discussion thereof. (That's why there's a separate meta.stackoverflow.com domain.) And analogously to the Git commit history, your name is automatically stamped onto your posts, along with a link to your site profile, in a box at the bottom of the post.