Custom theme doesn't show up in Blocks section-Collection of common programming errors

The error you are getting is caused from the fact the name is missing from the .info file for your theme.
In block_menu(), the code that is causing the error is the following one.

$items['admin/structure/block/list/' . $key] = array(
  'title' => check_plain($theme->info['name']), 
  'page arguments' => array($key), 
  'type' => $key == $default_theme ? MENU_DEFAULT_LOCAL_TASK : MENU_LOCAL_TASK, 
  'weight' => $key == $default_theme ? -10 : 0, 
  'access callback' => '_block_themes_access', 
  'access arguments' => array($theme), 
  'file' => 'block.admin.inc',
);

$items['admin/structure/block/demo/' . $key] = array(
  'title' => check_plain($theme->info['name']), 
  'page callback' => 'block_admin_demo', 
  'page arguments' => array($key), 
  'type' => MENU_CALLBACK, 
  'access callback' => '_block_themes_access', 
  'access arguments' => array($theme), 
  'theme callback' => '_block_custom_theme', 
  'theme arguments' => array($key), 
  'file' => 'block.admin.inc',
);

In system_menu(), the code causing the error is the following one.

  foreach (list_themes() as $theme) {
    $items['admin/appearance/settings/' . $theme->name] = array(
      'title' => $theme->info['name'], 
      'page arguments' => array('system_theme_settings', $theme->name), 
      'type' => MENU_LOCAL_TASK, 
      'access callback' => '_system_themes_access', 
      'access arguments' => array($theme), 
      'file' => 'system.admin.inc',
    );
  }

In all the cases, the error is raised when Drupal tries to access $theme->info['name'], but the “name” index is not defined.

Be sure there isn’t any strange Unicode character before name =, especially an invisible character.

If you are editing the .info file of the theme when the theme is enabled, you need to first disable it, and re-enable it, as the content of the .info file is cached.