How do I access the view block name?
I'm not really sure this is correct, but I guess you are looking for the id for the block:

function THEMENAME_theme_suggestions_views_view_alter(array &amp;$suggestions, array $variables) {
  if (isset($variables['view'])) {
    $view_id = $variables['view'];
    $id = $view-&gt;id();
    $block_id = $view-&gt;getDisplay()-&gt;display['id'];
    array_splice($suggestions, 1, 0, 'view__bundle__' . $view_id . '__' . $block_id);
  }
}


You can also print out the contents of the $view-&gt;getDisplay()-&gt;display array to check for other values that you might use.