What is called when people decide for themselves under what government they wish to live?

It depends how you define "government".

If you are referring to government as a "regime type", the choice between regime types rarely ever happens, but there are some exceptions, such as when Italians narrowly voted in 1946 to become a republic (as opposed to a constitutional monarchy). Such a popular vote is often called a "constitutional referendum".

If you are referring to government as "the political parties elected to power", when people have such a system, it is called a democracy. If groups other than the general population make such choices, i.e. the military chooses, wealthy individuals choose, etc., this is not democracy.