There are a couple of ways you can edit a contact's profile: Via the HUB (Recommended - click HERE for these instructions), via the Legacy app (Option 1), and via the Contacts Page (Option 2).
Option 1: Legacy Inbox
In the inbox search bar, search for the contact by their name or phone number.
On the far right side of the screen, you will see all of the contact's information. Here you can edit the contact's name, email, birthdate, tags, groups, or notes.
Make sure you click "save" when finished.
To block/unsubscribe/delete a contact
Blocking a contact keeps them from texting any of your numbers. It works just like it would work on your phone to block a person.
Unsubscribing a person opts them OUT of receiving messages from you but does not block them from texting you, and they are still able to opt back in if they want later.
Deleting removes the contact from your contact list.
Option 3: Via the Contacts Page
Search for the contact in the top right corner.
Then click the "edit" icon next to the contact you wish to edit.
*Side note: Click the "view" icon to view the contact's details, view chat, block, delete, or unsubscribe this contact.
You will be able to edit all the contact's information in this screen. Make sure and scroll down to the bottom and click save.