Can drush show list all available modules? With yum you can do yum list available ..., and know the name of the package you want to install. 

For example, there is the Mime Mail module in Drupal. What name should I use with drush dl, mime_mail, or mimemail? 

So does drush have something like yum list available?
No, drush can't do that.

Why should it when you can see the entire list yourself on drupal.org.