Why does my Arxiv paper not show my affiliation?
By default, the Arxiv does not show affiliations of paper authors on its webpages. You apparently can add them by adding them in parentheses behind your name. See the help pages:


  If you wish to include author affiliations, put them in parentheses. Do not put a full mailing address. At most, include a city and country (no zip codes, postal codes, or street addresses). If you have several authors from the same institution, you can use a footnote style for the affiliations. Here is an example (be sure to do it in the form presented here, including all parentheses, and using numbers and not letters):

  Authors: Author One (1), Author Two (1 and 2), Author Three (2)  
          ((1) Institution One, (2) Institution Two)



However, this feature is rarely used in my experience.

However, on the actual preprint (i.e., the PDF, PS, or whatever), you can show affiliations as you like (well, they should be correct). These are not automatically added by the Arxiv; you have to do this yourself. The content and layout of the actual preprint is controlled by you (except for a watermark from the Arxiv).