Stern acquired the Godzilla license, I think Dwight Sullivan has said they don't acquire licenses to NOT use them, and it would be strange to use the title of a machine you've built or are going to build as the code name for another machine. For that reason, it seems unlikely they'd use Godzilla as a code name. Similarly, it's also why I doubt a Jaws machine is coming because it was used as a code name for Jurassic Park.

Obviously I don't know anything for certain, but that's just my two cents.