Every person can have just one lega name. No more. Does not matter in which country you legaly change your name. Your name is changed. And you have a legal obligation to notice a second country. In the most countries, it is possible to change a name by a court hearing case. You will receive resolution issued by the court. You have a legal obligation to notice every other country, where you have issued passport, ID, immigration card, drivers license about this change. By the law of the most of countries, from the moment of name change, documents with previous name are invalid, or valid for som short period like 72 hours - to give you way how to travel back..