People have dumbed down the Turing Test. The original was a party game like Werewolf/Mafia.

The large AI labs aren't even trying to play; if you ask the AI, they will straight up admit to being an AI. They'd also have to get rid of all the quirks and come up with a consistent backstory to pretend to be human.

At least we're not thinking that it is God. Is there a name for that test?

That was always what the turning test was, even according to turing ...