What is the name of the villain in the Sherlock Holmes story 'The Final Problem'?

The villain in Arthur Conan Doyle’s Sherlock Holmes story The Final Problem is Professor Moriarty.

Professor James Moriarty is portrayed as a criminal mastermind who directs a vast organization from behind the scenes. Holmes describes him as a former professor of mathematics whose extraordinary intellect has been devoted to crime. Rather than committing every offense personally, Moriarty plans operations, protects criminals, and shares in their profits.

The story, first published in 1893, was designed as a climactic confrontation between Holmes and his most formidable enemy. Holmes traces Moriarty to Switzerland, where the two struggle beside the Reichenbach Falls. Watson arrives too late and believes both men have fallen to their deaths. Doyle later revived Holmes, but Moriarty remained dead in the canonical narrative.

Readers sometimes confuse Moriarty with Colonel Sebastian Moran, another major criminal associated with Holmes, or with Mycroft Holmes, Sherlock’s exceptionally intelligent brother. Irene Adler is also not a villain in this story; she appears in a different Holmes adventure.