The investors in the British television programme are called Dragons because the programme itself is titled Dragons' Den.
In the show, the word “Dragon” is the programme's metaphor for an investor with money, commercial experience and the power to negotiate. Entrepreneurs enter the den seeking funding, and the panel assesses their idea, finances, valuation and proposed ownership share.
The label is specific to the branding of the British edition and related versions using the Dragons' Den title. Other adaptations use different animal metaphors; the United States version, for example, is called Shark Tank and calls its investors sharks.
This distinction matters because “Dragon” is not a formal financial job title. It is the show's branded term for its investor panel, whose members may be entrepreneurs, retailers or business executives.