How do I send PayPal the Craft Commerce Order Number?
Commerce V1 - You can use a hooks for this:

https://craftcommerce.com/docs/hooks-reference#commerce_modifygatewayrequestdata

or

https://craftcommerce.com/docs/hooks-reference#commerce_modifypaymentrequest

...basically, start by dumping all the data to look at what is being sent, then modify it as you need.  Here's an example of something similar (I truncate the data to make sure it fits the gateway's limits):

    public function commerce_modifyGatewayRequestData($data,$type,$transaction){

        # Dump the data to see what is there....
        BusinessLogicPlugin::log("commerce_modifyGatewayRequestData"); 
        BusinessLogicPlugin::log("data");
        BusinessLogicPlugin::log($data);
        BusinessLogicPlugin::log("type");
        BusinessLogicPlugin::log($type);
        BusinessLogicPlugin::log("transaction");
        BusinessLogicPlugin::log($transaction);

        # TRUNCATE any over-sized data eWay might not like....
        # Data limits come from here: https://eway.io/api-v3/#direct-connection

       if(isset($data['Customer']['FirstName']))
        $data['Customer']['FirstName'] = substr($data['Customer']['FirstName'], 0, 49);

       ... etc

      return $data;
   }