You have the line AND ( @BG = ''''OR COM.BGName =''' + @BG +'''. `@BG' isn't declared in your Dynamic SQL. You need to pass it like you did later in the same line:
AND ( '' + @BG + '' = '''' OR COM.BGName =''' + @BG +'''
This query, however, appears to be open to SQL injection; you would be much better off parametrising it:
SET @query = N'
SELECT ComponentName,
'+ @cols + N' --This might need to be changed as well, but i don''t know how you''re generating this and I''m not guessing
FROM (SELECT SUM(('+ @Sum_cols + N') AS Comp_stock, --This might need to be changed as well, but i don''t know how you''re generating this and I''m not guessing
Com.ComponentName,
BB.BB_Name
FROM Z_DM_DR_CM_STOCK COM
INNER JOIN BLOOD_BANK_MASTER BB ON COM.BB_srno =BB.BB_SRNO
WHERE Com.Trans_date = @sTrans_date
AND (@sBG = '''' OR COM.BGName = @sBG )
GROUP BY Com.ComponentName,
BB.BB_Name) AS sourcetable
PIVOT (
--This might need to be changed as well, but i don''t know how you''re generating this and I''m not guessing
SUM([Comp_stock]) FOR [BB_Name] IN ('+ @cols + N')) AS PIVOTTABLE
ORDER BY ComponentName';
EXEC sp_executesql @query, N'@sBG int, @sTrans_date date', @sBG = @BG, @sTrans_Date = @trans_date; --I have guessed your data types
Note (as I know people have a habit of not reading comments people leave for them in their code) I have no idea what the data type for @BG and @Trans_date is, thus I have geussed they are int and daterespectively. You'll need to changed this, if i have guessed incorrectly.
You can see from the comments that you need to looks at how you add the values of the columns to your query as well; the way you've done it may also be open to injection, but i haven't seen the earlier part of your query.
@BG= ''''OR COM.BGName =''' + @BG +''' here @BG is included in string