What is the name of the detective in 'The Secret of Chimneys'?

The detective in The Secret of Chimneys is Superintendent Battle.

Battle is a Scotland Yard superintendent who leads the principal police investigation after a murder at Chimneys, the country house at the centre of Agatha Christie’s 1925 novel. The book introduces him alongside Lady Eileen “Bundle” Brent and begins Christie’s recurring Superintendent Battle series.

Anthony Cade, the adventurous central character, also investigates events and uncovers important information, so readers may remember him as the story’s active amateur sleuth. However, Cade is not the official detective named in the question: Battle directs the formal murder inquiry and works through the novel’s political intrigue, disguises and coded clues.

The Secret of Chimneys was published in June 1925 and was followed by The Seven Dials Mystery in 1929. Battle later appeared in Cards on the Table, Murder Is Easy, and Towards Zero. Miss Marple and Hercule Poirot are not characters in the original novel, although later adaptations sometimes alter Christie’s cast.