No they don't. The only unconventional term is NA-T referring to a 7MGE or 2JZGE that has been custom turbo'd. Common usage is simply 1JZ or 2JZ, automatic implication usually being that it is tubo'd. When specifying a setup you will hear '1JZ with stock twins', '2JZ with big single' never '2JZGTTE'.
2JZGTTE = Noob speak.
And referring to a 2JZGE/NA-T as a 2JZGTE is also a fail.
You are henceforth educated.