The country can't (directly) control how it is called in another languages, but if the language is the official language of an international organization that country is a member of, it has potentially more control.
How it looks like by official English country names in United Nations. Let's say the country A is not happy with its English name and want to be called otherwise (for example, Georgia wants to be called Sakartvelo). Is there any standard procedure of such name change, or such cases are not regulated and will depend on situation?
Of course the country would have no direct influence how it will be called by English speakers of another countries, it could only lobby for it.
The background of the question is the real-case of Georgia not happy with its name in many languages coming from Russian (http://www.telegraph.co.uk/news/worldnews/europe/georgia/8603300/Georgia-lobbying-countries-to-adopt-name-change.html) and an off-topic but interesting question about Czech Republic on Trave.SE (https://travel.stackexchange.com/questions/100834/czechia-or-czech-republic-or-both).