How can I edit the name provided in the billing block for an event registration?
Graham,

You will have the issue with first and last name no matter where users enter the information. The name is entered as the contact name and the billing fields are just pulling the data for the billing address.  I would like at the Civi Normalize Extension (https://civicrm.org/extensions/normalise-data-entered-firstname-last-name) to help you with this. 

Thanks,
Steve