If this user  is created  in Active Directory and Sharepoint is refreshing from active directory, then changing the display name in Sharepoint will change  it temporarily. But when Sharepoint refreshes or syncs with Active directory the next time, the name will be changed back to what is in Active Directory. For a permenant change in display name it has to be changed in AD.

All this is assuming that you are using AD to create accounts and authenticate.

I was wondering when does sharepoint refreshes.. how can i set-it to automatically refresh; I believe our system administrator did not set this..

In testing this out, it is important to remember that the profile information is overwritten only if the profile field is mapped to an AD user  account property. If the field is not mapped to an AD property, then it cannot be overwritten by the profile update import.

Did you get the answer you are looking for with this?

To establish an Import Schedule for Active Directory:
1. site settings > manage profile database (under "user profile, audiences and personal sites)
2. Configure Profile Import
3. Determine a schedule that best fits your needs. I personally run mine once a day before the business morning (example 3am)

Hope this helps. If you are working a lot with audiences you will also need to establish a "compilation" schedule sometime after the AD import to insure your audiences reflect the most recent changes.

I was wondering if anyone else has experienced this...We initially were doing a
full import from AD. We tried to switch to an incremental import but got an AD
permissions error.

The address could not be found, (0x80044011 - You do not have sufficient
permissions for incremental import, or the DirSync cookie stored in the user
profile database is corrupt. If you are importing from a Windows 2000 domain,
check that the import account  has the Replicate Changes permission for Active
Directory directory services. If the import account has the permission, start a
full import to refresh the cookie. )