How to reformat HTML output of format?
You could do this easily with jQuery, check the .wrap() method:

$('blockquote').wrap('&lt;div class="name"&gt;&lt;/div&gt;');


The wrap() method will wrap elements into another element.

If you want to do it as custom CKEditor plugin I would look at an existing plugin that does something similar and modify it to get the markup you want. I found a Drupal module with a custom plugin that add a wrapper element to blockquote: https://www.drupal.org/project/ckeditor_blockquote_attribution