I see, you're western people, so you don't get used to Asian or Japan's tradition. You don't know the difference between calling by "title" and "nickname".
Calling a person by just his/her title without a name is to show respect to the person who are not close to you in Asia, but this kind of calling is not available in western countries. So, you misunderstand it as a nickname. No, it's not. LOL
To give you a picture, western people call their teacher by his/her name, right? But Asian people will call a teacher by his/her title without his/her name. It's like you call "teacher" instead of "Ms./Mr. name" It's normal in Japan but may be weird in western country. LOL
So, in Japan, you can see their relationship by noticing how they call the person.
The same example, if you're new to a teacher, you'll call him or her "sensei" without his or her name. But then you become closer, you'll call him/her by his/her last name with a suffix "san". And then you become very close to the teacher, you can call him/her by his/her first name with a suffix "o" or "ko". There are steps of relationship. You cannot skip the step because it's impolite. LOL
Fumi call Shinobu "director" which is a title, not a nickname. It means she's on the first step of relationship like you call your new teacher "sensei" without his or her name. If she create a nickname for him, it must be "Mr. director" instead of just "director." So, Fumi calls Shinobu following the tradition.