As far as I know, most of the countries in the world use "city government" to this end and some in the US use "city council".
But lately when visiting Bangladesh, a country in south Asia that is a former colony of Britain and part of the old India, I saw many official documents affixed with the sign of "city corporation" and the public properties on the street like the rubbish can marked with the same words.
My reaction was like, What is it? A city now becomes a company? I asked some local people but they either do not know English or they do not really know it means because such a name has existed for a long time.
So far I do not find any satisfying answer to that question in my search.
So is "city corporation" the right name in English for a city management team?