What do call them you when you have your own room in powerful Business?

It's just called a private office.

At some companies, every employee has a private office.

At other companies, you might get a private office because you need to make confidential phone calls or need more privacy than other employees.

Or it may be because you are a manager and this is a perk of being a manager.

You might manage people (employees) or a specific function

It's different in every company.