Airlines have their own 'callsigns' unique to that airline (eg. 'Speedbird' for British Airways, 'Baby' for BMIBaby). If the airline name is short then often just the name is used as the callsign (eg. Electra 512 would be Electra Airlines flight 512). It depends what the airline have registered as their official callsign. In theory anyone can have a callsign if it is registered, so perhaps I could go for 'BigAlOne'...
In General Aviation, the initial call to ATC etc would be the full callsign of the aircraft (registration) so if flying a UK registered aircraft it would be 'Golf - X-Ray Uniform Alpha Whiskey' for G-XUAW.
If flying an aircraft that is non-UK registered then (stating the obvious) it would be different, eg. in the USA when learning to fly I was using callsign of 'Cessna Five-One-Seven-Two-Bravo' when I was flying N5172B, a Cessna 152. However in the event of an emergency the 'Cessna' would be dropped in the callsign, which would then be given as 'November Five-One-Seven-Two-Bravo' with the aircraft type being given as part of the emergency call.
I'm not sure if this is standard US practice, but was the way I was taught. I heard some people using callsign N-XXXXX and some using 'Citation XXXXX or Warrior XXXXX etc. so there seemed to be a mix of the way it was done. Perhaps a US-based PPruner would like to straighten that one out if there is an 'approved' method..?
The pilot of an aircraft must NOT abbreviate the callsign until the air traffic unit has done so. So you are not quite correct when you say that the subsequent calls are 'Golf - Alpha Whiskey' (in the above example). There are also incidents (eg. when reading back a departure clearance) when the full callsign should be used even if abbreviations have already been used in RT calls to/from ATC.
'Tyro' is actually a military term used to identify an inexperienced pilot but this would be widely recognised by most (if not all) ATC in the UK. To my knowledge it is a UK term and so may not be recognised abroad. As I understand, the only time 'Tyro' is used is when declaring an emergency using a 'Pan' or 'Mayday' call, to indicate to the ATC unit that the pilot is inexperienced. This helps ATC avoid giving any complex instructions or too much information to allow the pilot on concentrating flying the aircraft.
Now realised that FFF has jumped in and answered your question ahead of me but hopefully between us we have been of help!