Get the active menu parent from a menu block

Question

I'm attempting to use hook_block_view_alter() to set a block title to the name of the page's parent menu item.

The block is a menu block for the main menu that is showing second-level items.

I've found that this works to set the title:

/**
 * Implements hook_block_view_alter().
 */
function nama_components_block_view_alter(array &$build, \Drupal\Core\Block\BlockPluginInterface $block) {
  if ($build['#id'] == 'nama_d8_main_menu') {
    $parent_menu_item = 'just testing!';
    $build['#configuration']['label'] = $parent_menu_item;
    $build['#configuration']['label_display'] = 1;
  }
}

From here, how would I look up the parent menu item from the block so I can actually set $parent_menu_item? I've looked through what I'm getting in the $build and $block parameters, but I'm just not seeing it.