While you are enabling Avalara as your preferred mode of tax calculation for the EU region, you will be prompted that the Tax Registration Number specified will be displayed on your customers' Invoices.

If you have registered for VAT MOSS, you can enter your registration details and click Proceed. You can even add tax registration numbers for specific countries if required.

If you haven't registered for VAT MOSS, you will be prompted to add tax registration numbers manually, for countries where you have registered for VAT.

Note: While configuring tax codes
- It is recommended that you specify tax codes for your plans and addons for the EU region.
- Avalara identifies digital and physical goods only using these tax codes, based on which different taxes and exemptions are applied. 

Click this link to read more.