Babylon city was the capital of the Babylonian Province, and is depicted in the following....

While the capital city of Babylon is in ruins, Baghdad and much of the Southeast part of modern day Iraq can be considered to be part of "Babylonia."  Now it is really a translator's choice as to whether to render it as "Babylon" or "Babylonia" in English.  You don't get all that much confused when you talk about New York, New York in the USA, do you?  Having a city name that is the same as the name of hte state it is located in is not all that confusing for those of us who live there all our lives.  We can usually tell from context whether someone is talking about the Long Island city or the greater state.

Shalom, Joe