Once you've purchased an iPhone 16 or 16 Pro Max, it's important to understand that changing the name on the invoice after the purchase is not possible. The name listed on the invoice, even if incorrect, is not relevant for future trade-ins, refunds, warranty claims, or exchanges with Apple. Apple's policies do not require the name on the invoice to be accurate for these processes, so you won’t encounter issues related to this when dealing directly with Apple.
However, if you need the invoice for any claims outside of Apple Store-related activities, such as for a third-party store or another business, you will need to contact the store where the purchase was made. They may be able to assist you in correcting the name on the invoice. If the name error was their fault, they might be able to issue a new invoice with the correct details. If the store is unwilling or unable to assist, it might be helpful to explore whether you have any alternative documentation that proves the purchase.