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In English, the following is grammatically correct:
Am I going to the cinema today?
In contrast, the assertion that this is true is grammatically correct only with the first two words reversed.
I am going to the cinema today.
Does this phenomenon have a name, and is it linguistically common?
This is generally called subject-auxiliary inversion: it's a syntactic phenomenon (i.e. having to do with how words are put together) that's best-known from English but also appears in other Germanic languages (cf Standard German Du bist ein Amerikaner "you are an American" vs bist Du ein Amerikaner? "are you an American?"), and it's started to spread from the Germanics to other languages of Europe.
(The reason it's called subject-auxiliary inversion instead of subject-verb inversion is because when you have an auxiliary along with the verb, only the auxiliary moves: "you have been to Europe" vs "have you been to Europe?", for example.)
Outside of Europe, it's not particularly common for questions, but switching the order of phrases is used for other things: in Lingála (a Bantu language of the Congo), for instance, the subject and verb can switch places to indicate a relative clause.
