function THEMENAME_preprocess_html(&$vars) {
  if ($vars['is_front']) {
    $vars['head_title'] = variable_get('site_slogan', $vars['head_title']);
  }
}

function THEMENAME_preprocess_page(&$vars) {
  if ($vars['is_front']) {
    drupal_set_title($vars['site_slogan']);
  }
}

Drupal 7.x