Grigory S.

add_filter('render_block', 'wrapBlock', 10, 2);

function wrapBlock($block_content, $block)
{
    $name = $block['blockName'];

    if ($name)
    {
        return sprintf('<div class="e-block e-block-%s">%s</div>', str_replace('/', '-', $name), $block_content);
    }

    return $block_content;
}