Damn browser crash!
Anyway, I don't think it really had an official code name (at least none that I'm aware of). The architecture did go by the name "C62" when it was in development at Hudson, and unofficially as "HuC62", "HuC", and the "62".
Some of the various major chips had nicknames as well;
CPU: HuC6280
AKA: Dr. Pepper
VDC: HuC6270
AKA: 7up
CPE: HuC6260
AKA: Testukannon (Iron Goddess of Mercy)
The last is rather funny since the PC-FX was also known as "Tetsujin" (Iron Giant)...