What is the name of the Pinkerton detective in 'The Valley of Fear'?

The Pinkerton detective in “The Valley of Fear” is Birdy Edwards.

Edwards works undercover for the Pinkerton Detective Agency and infiltrates the violent Scowrers, a secret criminal organisation operating in the fictional Vermissa Valley. To enter the gang, he adopts the identity Jack McMurdo and presents himself as a new arrival with links to the organisation’s criminal world.

The novel’s first section frames Edwards’s investigation through the murder mystery at Birlstone House. John Douglas appears to have been killed, but the later backstory reveals that Douglas is actually Birdy Edwards living under another identity. His earlier undercover work exposed the Scowrers and helped bring their members to justice.

A common mix-up is to answer Jack McMurdo or John Douglas. Jack McMurdo is Edwards’s undercover alias, while John Douglas is the later identity he uses in England. Birdy Edwards is the detective’s real name, making it the canonical answer to the question. The novel was Doyle’s fourth and final Sherlock Holmes novel.