I recently upgraded to iOS9, and sometime after that (it might have been immediately after the upgrade or a short time after the upgrade but I'm not sure), I noticed that when I received phone calls and text messages, I would only see the phone numbers of the callers and senders but not their actual names. It turns out that some (but not all) of my contacts disappeared. So in an attempt to re-synchronize my contacts from my iMac where all of my contacts remained intact, I plugged my iPhone into my iMac and synchronized through iTunes, but to no avail. Rebooting the iPhone didn't help either. I searched online for solutions, including an Apple discussion forum (https://discussions.apple.com/thread/7221426) and this trick to force contacts to sync (http://www.macobserver.com/tmo/article/ios-refreshing-icloud-contacts-calendars), but nothing worked.
Your results my vary, but here's what worked for me. I simply created a fake contact in my iPhone Contacts application, and that resulted in a synchronization as evidenced by the spinning icon. This went on for about a minute, after which all my contacts in my iMac re-appeared in my Contacts app on my iPhone, and my Phone and Message apps displayed names once again. After that, I deleted my fake contact, and order was restored to my universe.
