Please, read my comment to the question first.
I've created sample script. Feel free to change it to your needs.
DECLARE @table1 TABLE(narration NVARCHAR(100), [match] int)
INSERT INTO @table1(narration)
VALUES('NEFT/N292190958364579/00019049/NILESH R DESAI'),
('NEFT/N292190958345310/00019049/NILESH H DELHI'),
('NEFT/N292190958345325/00019049/NILESH O BARAI')
DECLARE @table2 TABLE(narration NVARCHAR(100), [match] int)
INSERT INTO @table2(narration)
VALUES('To-Trf. RTGS : BAJAJ FINANCE LIMITED 191 Cr A/c No 1011132001850 UTR N292190958345310'),
('Ot-Rtf. RSGS : DESAI FINANCE LIMITED 195 Cr A/c No 1011132001880 UTR N292190958345380'),
('Do-Zff. RTTS : BARAI FINANCE LIMITED 111 Cr A/c No 1011132001855 UTR N292190958345315')
DECLARE @common TABLE(narr1 NVARCHAR(100), s1 NVARCHAR(100), s2 NVARCHAR(100), narr2 NVARCHAR(100))
INSERT INTO @common(narr1, s1, s2, narr2)
SELECT t1.narration as narr1, t1.s1, t2.s2, t2.narration AS narr2
FROM
(
SELECT narration, SUBSTRING(narration, CHARINDEX('/', narration)+1, CHARINDEX('/', narration, CHARINDEX('/', narration)+1)-CHARINDEX('/', narration)-1) AS s1
FROM @table1
) t1 INNER JOIN
(
SELECT narration, RIGHT(narration, CHARINDEX(' ', REVERSE(narration))-1) AS s2
FROM @table2
) t2 ON t1.s1 = t2.s2
UPDATE t1
SET t1.[match] = 1
FROM @table1 t1 INNER JOIN @common t2
ON t1.narration = t2.narr1
SELECT *
FROM @table1
Note: i'm using temporary tables (stored in variables).
@common
table is used to grab common data, then to update table #1.
In the same manner, you can update table #2.
Good luck!
Result:
narration match
NEFT/N292190958364579/00019049/NILESH R DESAI NULL
NEFT/N292190958345310/00019049/NILESH H DELHI 1
NEFT/N292190958345325/00019049/NILESH O BARAI NULL