Step 1: The question links a specific functioning pancreatic islet-cell tumour to its eponymous syndrome. VIPoma releases vasoactive intestinal peptide, and the matching eponym is Verner-Morrison.
Step 2: Recall the secretory effect of VIP on the gut: it stimulates intestinal fluid secretion, producing a profuse watery diarrhoea that persists even during fasting. This loss of potassium-rich fluid leads to hypokalaemia, while gastric acid output falls, giving achlorhydria. The mnemonic WDHA (Watery Diarrhoea, Hypokalaemia, Achlorhydria) captures this, and pancreatic cholera is another name.
Step 3: Eliminate the wrong matches one by one. Gastrinoma maps to Zollinger-Ellison, not VIP. Serotonin and other amines map to carcinoid syndrome. Glucocorticoid excess maps to Cushing's syndrome. Only Verner-Morrison fits VIP.
Step 4: Most of these tumours are pancreatic in origin in adults, supporting the islet-cell tumour classification.
\[\boxed{\text{Verner Morrison}}\]