The DG at the top of the screen is the iPhone account holder’s initials. It’s a gray text box on the left-hand side of the phone so it’s likely an inline reply; IOW, a reply to DG not from DG.
It looks a little strange because the right and left edges of the screen shot have been ‘cut off’ a bit. Perhaps on purpose or purpose it’s an artifact of the Examiner publishing the image file. Hard to say, for sure.
The DG at the top of the screen is the iPhone account holder’s initials.
That's not how mine is set up. Is that an option in settings?
See here (the contact's info is at top, according to Apple):