There is no scalar variable $PLL_name, only the array. Do not use the same name for an array and a scalar, it only confuses humans.

Possible solution:

#!/usr/bin/perl

use warnings;
use strict;
use diagnostics;

use File::Copy;

my @IDI_names = ('I:\Production\TEST\P001.txt',      'I:\Production\TE
+ST\P002.txt'); 
my @PLL_names = ('I:\Production\TEST\ISBN_Text.txt', 'I:\Production\TE
+ST\ISBN2_Text.txt'); 


for my $idx (0 .. $#IDI_names) {
    my $IDI_name = $IDI_names[$idx];
    my $PLL_name = $PLL_names[$idx];
    copy($IDI_name, $PLL_name);
}
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Perl is not a shell. There is no need to double quote single scalar variables.