Are there any custom block type template naming conventions?
Here's one way to do it, in a module or theme:

function MYMODULEORTHEME_theme_suggestions_block_alter(&amp;$suggestions, $variables) {
  $content = $variables['elements']['content'];
  if (isset($content['#block_content']) &amp;&amp; $content['#block_content'] instanceof \Drupal\block_content\BlockContentInterface) {
    $suggestions[] = 'block__' . $content['#block_content']-&gt;bundle();
  }
}


Results in template suggestions like:

block--custom-block-type.html.twig

The instanceof might be overcautious, take it or leave it.