Name dialing field doesn't auto-update but you should be able to access it from the "User Configuration" Page. On the left hand side, you should see a link called "Auto Attendant". Click on this and you should then see the "Name Dialing" field. Make the necessary changes and click "Update".

The problem is that changing the first and last names in the CallManager user pages doesn't change the 'name dialing' field and there doesn't appear to be any way of changing this field to reflect the new first and last user names.