If you are shipping a Domestic First Class Envelope/Flat or shipping internationally using First Class Mail or Priority Mail service, you will not see your order number appear on the label as the USPS does not support this currently.
How to: Customize USPS domestic shipping labels
What is the Large Envelope/Flat?
Why is the postage cost showing on the USPS Large Envelope package type?
Why can't I track a USPS First Class Large/Flat Envelope shipment with the tracking number provided to my store?