the program has to find successful match if the filename is following
Case 1 : test_file_name.dat (all lower case)
Case 2 : TEST_FILE_NAME.DAT (all upper case)
Case 3 : Test_File_Name.dat (Mixed)
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Only those three combinations or also the many possible other ones like tESt_FilE_nAMe.DaT? (Even though they may not actually be there.) If the latter, than just use

lc $name eq 'test_file_name.dat'
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as test.

Update: not directly related to your problem but also:

    $datfile = uc(test_file_name.dat);
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use strict;    # and
use warnings;  # as well
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        open(FL, $File::Find::name);
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Just the usual recommendations:

1. use the three args form of open;
2. use lexical filehandles;
3. check the return value of opens.

Why are you opening it anyway? (Since you do not actually use it.)