Lägg till en WHERE
klausul
UPDATE dbo.TestStudents
SET LASTNAME = CASE
WHEN LASTNAME = 'AAA' THEN 'BBB'
WHEN LASTNAME = 'CCC' THEN 'DDD'
WHEN LASTNAME = 'EEE' THEN 'FFF'
ELSE LASTNAME
END
WHERE LASTNAME IN ('AAA', 'CCC', 'EEE')