If you want to avoid a table scan, you need to provide a where clause for the UPDATE statement. Give this a shot:
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');