To implement a more business focused strategy they need to add some more differentiation, skype-for-business-but-using-it-from-home, skye-at-work-but-not-for-business, skype-for-idiots, skype-for-discussing-problems-with-skype
All these will have to be registered to a single Office365 account but you can't have two different ones installed on the same machine at the same time. Obviously they can't call contacts on one of the others.
Logins will prompt you if this is a microsoft personal or work email address, which one you have to click will vary on a daily basis. Any support requests will require you to have either a hotmail or outlook.com address or both, or neither.