Any objection to calling it an EA14?
Other performance vehicles are often given nicknames based on their chassis codes (BNR32, FD3S, AE86, etc). The Civic Type R has had so many variations that the phrase "Civic Type R" means less than simply saying "EK9" or "FK8."
Assuming that GZ stands for "Gazoo," future generation GR Corollas, if any, will probably follow the GZXXXX nomenclature. I therefore propose "EA14" as the nickname for the E210-based GR Corolla.