Yes, you can add the company tax registration number in an invoice's header, Jessica.
You can go to the Custom form styles panel to customise an invoice and add the company registration number.
For more details about customising invoices, estimates and sales receipts in QuickBooks Online (QBO): https://community.intuit.com/articles/1768656.
I have articles here about customising sales forms:
I'm confident the steps I've provided can help add the company tax registration number in your invoice's header.
Please reply to this post if you need anything else with customising an invoice. I'm always here to help.