For contact name you can select Default settings, Redirecting, Redirection, Caller ID and Connected ID. Proper variant depends on your phone system. You should try all variants to setup contact name to be displayed properly.
New Contact
In Configuration => Call center => New Contact you can set up special contact names for unknown numbers. They will not be saved as New Contact. Dial IT will take contact name from Caller ID, Connected ID, Redirecting, Redirection or will use default settings.
See also
Call Center settings
Email-Report Settings
Multi Company Dialing