Well, this is actually quite simple...
Internally at VW, it's referred to as the 5K.
Before the KBA (Kraftfahrt-Bundesamt), it was called 1K. Why? It's quite simple... The 6th generation Golf is therefore a post-homologation for the 5th generation and not a new homologation.
This is possible because the basic components (the chassis) are largely the same.
Similar incidents have happened before.
The Golf 1 was the Type 17.
When the Jetta 1 was introduced, it was also referred to as the 17th model. However, it was internally always designated as the Type 16. The registration document indicated the model as 17, but the Vehicle Identification Number (VIN) showed 16.
Similarly, this was the case with the Scirocco 1+2 (and even the Corrado). Both had the type designation 53. The 1 had the 53, the 2 had the 53b, and the Corrado had the 53i.
EDIT:
The third character in the model designation indicates the body style.
1 = Limousine
2 = Split-level rear.
5 = Variant
1J1 = G4 Limo; 1J5 = G4 Variant; 1J2 = Bora (Jetta in the USA).