The official plural nickname for the investors on Britain's Dragon's Den is “dragons.” The title describes the powerful financiers who sit behind the table and decide whether to offer capital for an equity stake.
Each investor is individually called a dragon, and the programme's branding uses the term consistently in introductions, press coverage and episode descriptions. The metaphor signals formidable negotiators rather than a literal connection with animals.
“Sharks” is the familiar investor nickname in the American adaptation Shark Tank, while “tigers” belongs to the Japanese source title Money Tigers. Those terms explain why they are plausible alternatives, but Britain’s programme uses dragons.