Here is the fix!!!
Okay, here is how you fix this problem:
STEP 1. First you have to dial *228 on your iPhone 4S. You should note that *228 is a Verizon over-the-air programming number.
STEP 2. Wait for sometime until the system responds, then you have to press 1″ to Program or activate your phone.
STEP 3. After sometime the system will say, Settings updated. Then you have to wait until the call disconnects.
STEP 4. Now double click the Home Button of your iPhone 4S to open the Task Manager.
STEP 5. Now close Phone, Message, and Contacts Applications on your iPhone 4S.
STEP 6. After waiting for five minutes, open the Message App on your iPhone 4S to check the fix.
Thats it. In this way you can fix iOS 5.0.1 contact bug on your iPhone 4S. If you are not able to fix this issue after using the above steps then again you have to close the Message App and restart your iPhone 4S. It is expected that soon Apple will release iOS 5.0.2 to fix this issue.