I chose to use virtual in my business name because that is what I am, a Virtual Assistant. I think as the public becomes more educated on this title, it will become more accepted. And I don't want to be changing my business name in the future.
I too thought about the definition of not being "real". That can be seen in a whole lot of different perspectives. We are real, but not a "real" employee and so on. Another example of a personal choice.
So, educating society on this new, but not so new title, opens up a chance to market yourself.