SQL Server 2019

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CREATE TABLE tablename(Nam VARCHAR(10), Descrip VARCHAR(100), Val1 INT, Val2 INT, Status VARCHAR(10));
INSERT INTO tablename(Nam, Descrip, Val1, Val2, Status) VALUES
('Test1', '', 10, 100, 'OK'),
('Test1', '', 10, 5, 'False'),
('Test2', '', 10, 9, 'OK'),
('Test2', '', 10, 5, 'False');
4 rows affected

UPDATE t1
SET t1.Status = CASE
  WHEN EXISTS (SELECT 1 FROM tablename t2 WHERE t2.Nam = t1.Nam AND t2.Val2 > t2.Val1) THEN 'OK'
  ELSE 'False'
END
FROM tablename t1
4 rows affected

SELECT * FROM tablename


Nam
Descrip
Val1
Val2
Status


Test1

10
100
OK

Test1

10
5
OK

Test2

10
9
False

Test2

10
5
False