The address on an invoice is the one you choose at checkout. Saved addresses fill the checkout in for you.
Open Addresses in the sidebar.

Add an address
Fill in the form and save it. Tick Use this as my default billing address to have checkout choose it first.
Change or remove one
Each saved address can be edited or removed from its card. Removing an address doesn't change invoices already issued to it — an invoice keeps the address it was made out to.
Note
Buying as a company? Put the company name and, where it applies, its tax or VAT number on the address, so they appear on your invoices.