buzztone on "[Plugin: Contact Form 7] Changing who the contact form is sent from"

Yes - see Setting Up Mail. Collect their details in Form section of the CF7 interface e.g. [text* contact-name] [email* contact-email] and then add [contact-name] <[contact-email]> in Mail>From section.

May not work is your host does not allow emails to be sent from other addresses.