Yes, you’ll need to provide guests with an invoice at check-out, either on paper or by email (or both).
Booking.com cannot send an invoice to you or your guests. That’s because when a guest books your property, the reservation becomes a legal agreement between you and them. So it’s your responsibility to provide guests with an invoice.
Note: The point at which a guest is charged can have tax implications for you, so it’s important for you to understand how to handle VAT and local taxes.