You can edit the Contact details from the Job list by clicking on either:
Billing name, to take you to the Billing information in the drawer that opens on the right of the screen. Click the Edit pen to edit the Billing information.
Contact name, to take you to the Contact information for any contacts listed under that billing name. You can then click on the expand arrows to get the options for the intended contact, and click on the Edit pen to edit the details.
Click Save and then click off the drawer to close it.