After upgrading the logon will show -
username, password, and if you select options. the domain name. Typically in your example it would be just mycompany.
Mixed mode just means you have a mixture of Win2000 and WinNT domain controllers.
Native is all Win2000 domain controllers.
The domain can be accessed via mycompany or mycompany.com, Windows 2000 can resolve both. The network neighborhood will display it as mycompany.
Hope this helps