When you send a message through the Email to SMS service, the IntelliSoftware system will store the Contact Name if available in the email From field.
When a reply SMS message is received and passed back to you via email (SMS to Email service), the IntelliSoftware will look up for a stored Contact Name for the given mobile number. If the Store Number is available it will be included in the To address of the email.
To Summaries, to make sure the contact name is shown instead of the mobile number, make sure that you provide the contact name in the ‘To’ field of the original email sent to the IntelliSoftware system (in the Email to SMS request)