iPhone Contact Name Issue with Phone/Message app

Hi everyone,

I'm having this issue with my manufacture unlocked iPhone 5 running iOS 6.1.3. This problem has been reported in several places (even in iOS5) but I didn't found the solution still.

At first, all my contacts' numbers were saved without region code (i.e. +44, +1, …). Then I realized that the Message app didn't recognize the contact and display contact number with region code at the front (i.e. +44 xxxxxxxx) instead of the particular contact name.

And so I added in region codes to my contact numbers, the Message app displays the contact names correctly, but now, instead of the message app, the Phone app doesn't recognize the contacts. Every time I receive call from someone in my contact list, it displays the phone number WITHOUT the region code instead of the particular contact name.

So, if I saved my contact numbers WITH region codes, the Message app would work fine, however the Phone app wouldn't recognize the contacts and wouldn't show the contact name when receiving a call;
and if I saved my contact number WITHOUT region code, the Message app wouldn't recognize the contact and wouldn't show the contact's name, but the Phone app would work just fine.

For me, I've tried resetting network settings, resetting all settings, and even erase all content and settings, yet this problem still exists. I found a fix which is about dialling *228 and press 1, it wouldn't work for me since I'm not using Verizon.

Does anyone have the same issue? Any fix?