I also have 10.1.1. I'm using an iPhone 7 Plus. Have you tried resetting your device, then going back to Messages, and tapping and holding the little "head icon" until the options come up, then putting in the First, Last Name and clicking done?
Sometimes a reset will clear things up: Hold down the Home and Power buttons (or the Volume Down and Power buttons if you are using an iPhone 7), and continue to hold them down until the Apple appears (up to 30 seconds). Once the Lock screen displays, try adding the contact via Messages again to see if it works.
I was having a problem today with my Photo Stream photos that I have taken in the last couple of days not getting to my Mac. I looked at all my settings, turned Photo Stream off and back on, and then took my own advice and reset the iPhone. Voilà - the photos started showing up as soon as the reset initiated - even before the Lock screen displayed....(forehead slap!) 🙂
GB