I'm with Lowell on cleaning up the data.
However, this might help you, but you still have to review the matches given.
;With Table1([AppID],[Appname])
AS
(
SELECT 'Null','CSO Services Operations' UNION ALL
SELECT 'Null','CSP' UNION ALL
SELECT 'Null','AAC Claims Systems'
),Table2([AppID],[Appname])
AS
(
SELECT '1','Corporate Services Operations(CSO)' UNION ALL
SELECT '2','Credit Servicing Portal(CSP)' UNION ALL
SELECT '3','American Assuarance Company (AAC) Claims Systems'
)
SELECT *
FROM Table1
JOIN Table2 ON Table1.Appname LIKE SUBSTRING( Table2.Appname, CHARINDEX( '(',Table2.Appname) + 1, CHARINDEX( ')',Table2.Appname) - CHARINDEX( '(',Table2.Appname) - 1) + '%'