If you don't actually need the email address in the dropdown, then put Full Name in the Value field. If you DO need that email address for other reasons, then set the default value of your other text field to this statement:
Set Field's Value:
NameField
Contacts(Full Name) where (filter) Contacts(email_address) equals PulldownField.
You're basically telling your text field to default to the Full Name of the person in the contacts list where the email address in the contacts list equals the email address in the form (the one chosen in the pulldown).