Possibly Management Consultant. Business Consultant is vague as to what you really mean that the person is advising on. I an an Environmental Consultant, for example. My advice relates to environmental matters.
You could call someone a "Business Consultant" but the idea of "business" is vast and not very specific. I could, conceivably, declare myself a "Business Consultant" if my clientele for my services were only businesses, but it is relatively meaningless (does not declare what it is that I actually get consulted about).
If a person declares themself a business consultant, that means that they claim to be able to assist in pretty well any matter associated with business operations, and that is a pretty broad expertise to claim. People still do it, though.
To answer your question, there is no rule that says that a person is not or cannot be identified as a "Business Consultant". It is just more typical for the consultant to be more specifically identified as to area of expertise than simply "business". Which expertise would that be? it depends on the individual. I do not know what aspect of business operations or concerns that person would be best described by, so cannot offer an alternative.