Hi: I did what you said by adding the email address to each contact, but that made no difference. Still just getting just the number. Oh well.
Try adding your email address to the contacts listing that has your Phone Number so that you have both the phone number and email address in the same contacts listing on your iPhone and on your Mac. If Message finds an entry in Contacts that matches the incoming address it shows the name address and image (if any) from the listing in Contacts. Otherwise it shows only the sending address contained in the text message itself.