How do I change the VAT number on my invoice?

Are you asking about your business VAT number on an invoice for your purchase of an Apple product or service, directly from Apple? You may want to contact Apple Support staff about that: Contact Apple for support and service - Apple Support.

Remember you are not asking Apple here, and taxation issues are beyond the scope of these user-to-user forums. If Apple cannot help, inquire of the tax authority that is driving the need to change