What accounts for the two different spellings of Hanover and Hannover?

Hanover is the English spelling,as in 1636 the Duke of Calenberg moved his duchy there. It became known as the Duchy of Hanover. Hannover is the German spelling. The British House of Hanover should always be spelt this way.

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Many German cities have an English spelling, for example Munich, Nuremberg, Frankfort, Hanover. So the question is probably general: Why did the English make separate spellings for cities in Germany, France, Italy and other places in the world?

Same reasons as for the French use Londres, Douvres, Edimbourg, Pays de Galles and so on. (Not to mention Wipers...) That is, folk etymology, easing of pronunciation, variable spellings in earlier days anyway, and occasionally just sheer bloody-mindedness. In the early days of printing, spellings hadn't hardened (see Shakespeare, for example) and one spelling might take in one place, while in the place itself there could be changes. Also, look at the mess the Norman scribes made of English placenames in the Domesday Book. Speakers of one language hear other languages in terms of their own. Manx gives an interesting case of this - a Celtic language spelled more or less in English! For another set of examples, look at what the European settlers in North America did to both the Native American places and things, and the surnames of immigrants from strange places.