The company founded by Duncan Bannatyne and associated with health clubs is the Bannatyne Group. The group became a major part of Bannatyne's business identity and reflects the leisure and fitness interests for which he was known.
Bannatyne first became widely known through business ventures including care homes and leisure enterprises. The Bannatyne Group operates in the health-club and spa sector, linking his entrepreneurial reputation with fitness facilities rather than with a single Dragon's Den pitch.
The answer is sometimes shortened informally to “Bannatyne gyms,” but Bannatyne Group is the company name. “Bannatyne Fitness” and similar phrases may describe the business area without being the canonical corporate name.
This distinction also separates an investor's own company from companies in which he considered investing on television. Dragon's Den contestants present independent businesses; the dragons' biographies cover their pre-existing commercial careers.