$path = "/path/to/my/dir";

$latest_ctime = 0;
$latest_filename = '';

$d = dir($path);
while (false !== ($entry = $d->read())) {
  $filepath = "{$path}/{$entry}";
  // could do also other checks than just checking whether the entry is a file
  if (is_file($filepath) && filectime($filepath) > $latest_ctime) {
    $latest_ctime = filectime($filepath);
    $latest_filename = $entry;
  }
}

// now $latest_filename contains the filename of the file that changed last