Create new order status and assign to close state.
Check following url
Change order status
In this example they explain for pending status.
I think it may help you.
For change state, i think you need to add new action in dropdown and on select newly created action you have to write code for change state.
For add new label in action dropdown, please check following post. They have added "Invoice capture online ". Add you custom label.
In controller massInvoiceCaptureOnlineAction() write your logic for closed. Here is that code.
$orderId = YOUR_ORDER_ID;
$order = Mage::getModel('sales/order')->load($orderId);
Please Check massInvoiceCaptureOnlineAction() code, you will get order ids. You just have to replace capture invoice code with above code.
I hop this will help you.