There is limited ability to edit certain aspects of Contact Information within Conversations. To accomplish this do the following.

For example, you can add an Email address to the contact by clicking the Email bar in the area indicated by the red circle in the image and entering the new address.

You can also enter or change the phone number as well as add or remove any system tags.

Also, you have the option to turn on DND or Do Not Disturb, add them to an active workflow and edit the opportunity they are in.