Often times, a Subscriber will not have any personalized data such as name or email tied to their profile. If they respond with their name in an Inbox message, you can quickly add it to their Subscriber profile by clicking the gear icon at the top right of the message thread > click Edit Subscriber.
You can add first name, last name, and email. You cannot edit the number, as this is what determines the Subscriber. If you need to edit their phone number, simply delete the current Subscriber and add a new Subscriber with the updated phone number.