What is the name of a political regime where an Artificial Intelligence rules all and make decisions?
One very recent paper proposed the term "aicracy". It's too early to tell if this will take off (as a term).
Some users have suggested in the comments that this should be called dictatorship. I think that depends whether the people would accept being ruled by AI or not. There's actually a recent article on this (not using the term "aicracy" by the way), citing an actual survey.
The Center for the Governance of Change at Spain’s IE University polled 2,500 adults in the UK, Spain, Germany, France, Ireland, Italy, and the Netherlands in January . The results reflect an intense anxiety about the changes brought about by advances in tech, with more than half of respondents worried that jobs would be replaced by robots, and 70% saying that unchecked technological innovation could do more harm than good to society. Respondents also expressed concerns about the impact of digital relationships replacing human contact as more people spend time online.
Perhaps most interestingly, a quarter of the respondents said they would prefer AI to guide decisions about governance of their country over politicians. [...]
The study also found that respondents expected governments to reduce the disruption that technology might have on their lives with regulation, limits on automation, and support for people affected by job losses. This “highlights the paradox in which we live,” the authors wrote. “People are disillusioned with governments, yet at the same time ask them to tackle the societal and economic negative effects that emerging technologies might have.”
So yeah, some people would "welcome our machine overlords", but apparently most won't. Of course, it's all theoretical, since we don't have a real general-purpose AI and most of the stuff written on the topic seems to ponder whether it will accept us rather than the other way around...