How do I edit a block's default title? "Powered by Drupal" is a footer block I need to change to my name for my website.

How do I edit its default title?
In drupal6, you can go into the block admin screen for that block and change the title there.  If you are meaning the title/hover title for the drupal image itself, you can create a function in your theme's template.php file along the lines of:

function YOURTHEME_system_powered_by($image_path) {
  $image = theme('image', $image_path, t('Powered by Drupal, an open source content management system'), t('Powered by Drupal, an open source content management system'));
  return l($image, 'http://drupal.org', array('html' =&gt; TRUE, 'absolute' =&gt; TRUE, 'external' =&gt; TRUE));
}


and just change the t() functions in there to say whatever you want.

ADDITION:

A quick grep thru d7 suggests changing this...

/**
 * Returns HTML for the Powered by Drupal text.
 *
 * @ingroup themeable
 */
function theme_system_powered_by() {
  return '&lt;span&gt;' . t('Powered by &lt;a href="@poweredby"&gt;Drupal&lt;/a&gt;', array('@poweredby' =&gt; 'http://drupal.org')) . '&lt;/span&gt;';
}


in a similar way as described above would accomplish what you want, but yes, you would need to edit some code to do it in your theme.  

If that doesn't work, or you aren't confident enough to do that, you could just remove/disable the powered by drupal block itself and create another one with your own created by link in it.