Some Contact Names not Showing in Calls or SMS (iPhone 4S)

Although it works fine for most my contacts, some fail to show when calling me or sending me SMS on my iPhone 4S with iOS 5.0.1 (9A406)-

Meaning, I just get a "meaningless" number instead of a contact name, and can never tell who called me or sent me a message.

These are contacts that worked just fine in my previous iPhone 4.

Weird things:

1) if I type the number manually in the dialpad, it does show up the name in the small "subtitle" beneath it - meaning it does recognize it as being in the contacts.

2) Even if I add the incoming number to a new contact (or existing o contact, duplicating the already memorized phone number), it still doesn't show up as contact name - just the number as before.

3) Deleting and recreating the contact had no effect.

4) This happens for some contacts but not others, in the same phone operator and similar phone prefixes.

5) Adding/removing the international prefix makes no difference (some "unknown" numbers shows without, other with country code - having both variations in the contact list makes no difference)

This is the kind of really basic stuff one would expect any simple cell phone to handle flawlessly... let alone a high-end device like an iPhone 4S!

I feel like I've got 20 years back in time, to my first motorola cell phone which didn't do this...