How do I name a mimemail-message.tpl.php template to be used with a specific webform?
As you can see in line 264 of webform.submissions.inc Webform uses submission as the key.
Thus it needs to be named
mimemail-message--webform--submission.tpl.php

There is no way to target a specific webform without some extra custom code work.
mymodule.module
function mymodule_mail_alter(&amp;$message) {
  if ($message['module'] == 'webform') {
    $nid = $message['params']['node']-&gt;nid;
    $message['key'] = $nid; // set key to nid
  }
}

Now you can do
mimemail-message--webform--250.tpl.php