iOS 9.1 vs iOS 9: What’s New in iOS 9.1

Show or Hide Contact Photos in Messages

With iOS 9 Apple added contact photos to conversations in iMessage. With iOS 9 there was no way to turn this feature off, but now Apple is allowing users to toggle this option in Settings.

Go to Settings -> Messages -> Show Contact Photos -> Off.

After you turn this off you will no longer see photos or initials in the Messages main screen on your iPhone.