What to call it? Personally, I don’t care for calling virtualized data centers “Private Cloud”. I prefer “Data Center Optimization”. And when you go beyond simply virtualizing SQL Server instances into automation, provisioning templates, self-servicing, billing, etc. you’ve definitely implemented a more optimized, streamlined data center.
This is what is being called a “Private Cloud”. But that is a fluffy term that does not say anything about the optimization of the data center or of the database.