The GT-R's original Godzilla nickname obviously comes from the iconic giant monster, but it's not really the right way to describe Nissan's sports coupe. Godzilla is certainly powerful, but he clumsily lumbers around, which is nothing like the way the GT-R behaves on the road.
If you want to use a giant monster for the nickname, I say pick Gyaos. This giant beast is the villain in the best of the Gamera films. With an appearance somewhere between a bat and a pterodactyl, it can fly at incredible speeds – like the GT-R on the road. Plus, Gyaos feeds on blood, similar to the blood-thirsty feelings drivers get when the GT-R launches away from a stop light and leaves all other traffic in its dust.
See if you agree by watching Gyaos fight in the clip below.