When sending shipments to outside of the EU, DPD.ie required a sender's EORI (Economic Operator Registration and Identification) or VAT number. This is required to be provided on the documentation that is supplied along with your goods to the destination customs.
If you need to add your EORI or VAT number to your Shiptheory account details, you can follow this guide on how to do so: http://support.shiptheory.com/a/solutions/articles/24000038147