I'm horrible at explaining, but let me try:
"The Americans" is a TV show about KGB spies in the US. Whenever there is a scene at the Soviet embassy, the actors start talking Russian. Now what strikes me as odd is, that they never address each other with only their first name (Hello, Arkady Ivanovich Zotov) or only their last name (Hello, Mr. Arkady Ivanovich Zotov). Instead they address each other with their first and middle name, even when talking to a superior. (Hello, Arkady Ivanovich Zotov)
Is there a historical reason for that at all, or is it just something the creators of the show chose to implement?
That is the standard polite way to address a person in Russian. If you watch Russian/Soviet films, or read Russian classics such Dostoevsky, you will see how ubiquitous it is. Creators of the show certainly didn't invent it. Addressing someone by their first name is very informal, typically reserved for close friends. "Comrade Zotov" would have been acceptable in the context of the show but perhaps unnecessarily formal or impersonal for a colleague that you see on a daily basis. And as a small correction, "Ivanovich" is not middle name but a patronymic.
this is actually a very formal way to address someone in Russia. Teachers are addressed by their first and middle name, too.