How to edit the People (users admin view) to include filter by user name?
You can take a look at the Administration Views Module:


  Replaces administrative overview/listing pages with actual views for
  superior usability.
  
  Features
  
  
  Filter all administrative views via AJAX.
  Perform any kind of bulk/mass operations on items in administrative views.
  Filter content by title, node type, author, published status, and/or vocabulary.
  Filter comments by title, author, node title, or published status.
  Filter users by name, ban/blocked status, or user roles.
  
  
  *Note: If you are upgrading from an older version of Administration views and the default views have been overridden (saved in the
  database) you could encounter issues or not see any new changes unless
  you revert these views, so the default in-code views are used. This
  can be done in the views UI listing or using drush (drush cter
  views_view --module=admin_views)


By default it has a specific users view, but since it is a view, you can modify it.