use warnings;
use strict;
#use File::Copy;

foreach( sort map { chomp;s/_(\d)_/_0$1_/g;s/_(\d)_/_0$1_/g;$_ } grep {/^\d+_\d\d\d\d_\d+_\d+_\d+_\d+_\d+_Table/} <DATA> ){

    my $newname = $_;
    
    $newname =~ s/^[0-9_]+//;
    printf "%38s%38s\n",$_,$newname;
    
    ## rename here.
    #move $_, $newname or print "Error renaming <$_> $!\n";
}

__DATA__
Test file names
8_2007_5_22_15_34_23_Table_-_2007522_XYZ_W3.pdf
8_2007_5_22_22_34_12_Table_-_2007522_XYZ_W3.pdf
8_2007_5_2_15_34_23_Table_-_200752_XYZ_W3.pdf
8_2007_5_2_22_34_12_Table_-_200752_XYZ_W3.pdf
8_2007_5_2_5_34_23_Table_-_200752_XYZ_W3.pdf
8_2007_5_2_2_34_12_Table_-_200752_XYZ_W3.pdf
7_2007_5_22_16_35_23_Table_-_2007522_XYZ_W3.pdf
7_2007_5_22_23_36_12_Table_-_2007522_XYZ_W3.pdf

blanks and other things
0
8_3007
 &#8993;&#9675;{§}&#9562;