Ute is short for Utility. We don't have many special name for each model they normally just call them after the sedan they are based on i.e. Falcon Utility or Commodore Utility.
The enly ones that seem to get their own name are the super hot versions. HSV (Holden Special Vehicles) call their version of the Commodore Ute the "Maloo". The FPV version (Ford Performance Vehicles) is called the "Pursuit".
FPV
HSV
Cheers