The term “master carpenter” or “master carpenter” is not an official degree or certification that exists in the United States. The highest certification someone can obtain is that of official. Other countries, such as Japan, offer masters-level training. This certification is expensive and difficult to obtain.
Carpentry is a trade, not a professional industry. Either you do it as a business or you don't. If you do it as a business, then you own a business that is a carpenter. If you don't do it as a business, then you're an amateur.
If you're doing it for a business, then you're an employee who's a carpenter. There is no such thing as a professional carpenter. Either you're good at the kind of work you do or you're not. Personally, I don't see any reason for a label.
I own a business that makes cabinets and furniture.