Final answer:
Sirius Black is first mentioned in 'Harry Potter and the Prisoner of Azkaban', the third book of the series, in Chapter 2 when the Minister for Magic discusses his escape from Azkaban.
Step-by-step explanation:
Sirius Black is first mentioned in "Harry Potter and the Prisoner of Azkaban," the third book of the Harry Potter series by J.K. Rowling. His name appears early in the book when Harry overhears a news report about a dangerous convict, Sirius Black, who has escaped from the wizarding prison, Azkaban.
The exact moment occurs in Chapter 2, when Harry is staying at the Leaky Cauldron and the Minister for Magic, Cornelius Fudge, inadvertently reveals Sirius Black's escape to him. This moment sets the stage for the central plot of the novel and is significant throughout the entire Harry Potter series.