$mbox = imap_open("{your.imap.host}","username","password",OP_HALFOPEN)
     or die("can't connect: ".imap_last_error());

$name1 = "phpnewbox";
$name2 = imap_utf7_encode("phpnewböx");

$newname = $name1;

echo "Newname will be '$name1'<br>\n";

# мы создадим новый mailbox "phptestbox" в вашей папке inbox,
# проверим его статус после создания и удалим его для восстановления
# вашего inbox в первоначальном виде

if(@imap_createmailbox($mbox,imap_utf7_encode("{your.imap.host}INBOX.$newname"))) {
  $status = @imap_status($mbox,"{your.imap.host}INBOX.$newname",SA_ALL);
  if($status) {
    print("your new mailbox '$name1' has the following status:<br>\n");
    print("Messages:   ". $status->messages   )."<br>\n";
    print("Recent:     ". $status->recent     )."<br>\n";
    print("Unseen:     ". $status->unseen     )."<br>\n";
    print("UIDnext:    ". $status->uidnext    )."<br>\n";
    print("UIDvalidity:". $status->uidvalidity)."<br>\n";
    
if(imap_renamemailbox($mbox,"{your.imap.host}INBOX.$newname","{your.imap.host}INBOX.$name2"))

    {
      echo "renamed new mailbox from '$name1' to '$name2'<br>\n";
      $newname=$name2;
    } else {
      print "imap_renamemailbox on new mailbox failed: ".imap_last_error()."<br>\n";
    }
  } else {
    print  "imap_status on new mailbox failed: ".imap_last_error()."<br>\n";
  }
  if(@imap_deletemailbox($mbox,"{your.imap.host}INBOX.$newname")) {
    print "new mailbox removed to restore initial state<br>\n";
  } else {
print  "imap_deletemailbox on new mailbox failed: ".implode("<br>\n",imap_errors())."<br>\n";
  }
  
} else {
  print  "could not create new mailbox: ".implode("<br>\n",imap_errors())."<br>\n";
}

imap_close($mbox);