“Alecto, Amycus’ sister, teaches Muggle Studies, which is compulsory for everyone. We’ve all got to listen to her explain how Muggles are like animals, stupid and dirty, and how they drove wizards into hiding by being vicious toward them, and how the natural order is being reestablished."
-- Neville Longbottom (DH29)
Alecto and Amycus Carrow were Death Eaters, a brother and sister, part of the group of Death Eaters that invaded Hogwarts in June of 1997 (HBP27); Snape implies that they were never sent to Azkaban (HBP2). Last name confirmed by JKR (JKR).
When Voldemort took over Hogwarts, Alecto Carrow became the Muggle Studies teacher (DH12). Before the final Battle of Hogwarts, Alecto was Stunned by Luna and then bound up by McGonagall and suspended in mid-air in the Ravenclaw common room (DH30).
Brother: Amycus Carrow
Pureblood racist, hated Muggles, loved punishing students
Alecto was one of the three Furies in Greek mythology. Her name means 'unceasing in anger' (EM).