One of the basic tenets of CQRS, as I understand it, is that commands should be behaviour-centric, and have a value in the business or the UL, and not data-centric, ie., CRU
CustomerHasMoved is the event that is fired after you have updated the customers location. This event updates the read databases/cache databases. The command from the gui should be MoveCustomer or something like that. I think I would put the update of the customer name in a command like UpdateCustomer.