What is a username exactly used for in arXiv? This is a fairly simple question, which any arXiv author could answer: the username set while registering in arXiv is not the authorial name users see when they read a paper you've published, right? The arXiv username set during registration is merely so that the author can log into arXiv?
Yes, that's correct. Here is my most recent paper, and you can't find my arXiv username anywhere on the page. 

There is a separate notion of "author ID", which is specifically for the purpose of collecting all your papers on one page, but you have to set that up separately afterwards. It's not the same as the username.