I still pose the question "why?" In social media, the reason you created your account is to socialize. I don't understand why in the context of developing and managing a business, one needs an anonymous profile.
There might be times when you want to communicate with people on a topic, without their being aware of who you are and what you do for a living, which could color the conversation or potentially even jeopardize your business.
Maybe you need to maintain contacts and industry awareness without alerting your competitors to your every move or to who your clients are. Maybe you are a victim of corporate espionage. Maybe you find yourself in the unenviable position of needing to both develop and manage a business and be a whistle-blower at the same time. There are any number of potential reasons.
We socialize without tieing things to our full name all the time. Why should online be different?