Canadians I believe only have C-Gxxx and C-Fxxx... ie, you will never ever see C-ABCD only C-GABC and C-FABC. This would be why it is truncated to 3 letters on first contact.
You arn't supposed to. On initial contact with ATS you must use all four letters (GXXX or FXXX) and continue to use all four until the ATS unit truncates it.. for example:
Pilot: Yazoo Tower Foxtrot Alpha Kilo Echo with information Yankee
Tower: Foxtrot Alpha Kilo Echo Go ahead
Pilot: Foxtrot Alpha Kilo Echo is 5 miles south of the field inbound for landing
Tower: Foxtrot Alpha Kilo Echo altimeter is 29.92 cleared to the circuit
Pilot: Foxtrot Alpha Kilo Echo
<later on in the circuit>
Pilot: Yazoo Tower, Foxtrot Alpha Kilo Echo is turning left base for runway 30 full stop
Tower: Alpha Kilo Echo cleared to land runway 30.
Pilot: Alpha Kilo Echo