You replied to a 4 years old thread. Moreover, you check half the pairs pointlessly - there's no need to check $arr[$#arr] versus $arr[0], when you've already checked $arr[0] versus $arr[$#arr]. Here's how I'd code your idea:

#!/usr/bin/perl
use strict;
use warnings;

chomp(my $name = <>);
my @arr = split //, $name;
my $is_palindrome = 1;

for my $i (0 .. $#arr / 2) {
    # warn "$arr[$i] eq $arr[ -$i - 1 ]";
    if ($arr[$i] ne $arr[ -$i - 1 ]) {
        undef $is_palindrome;
        last
    }
}

print 'Word is',
      $is_palindrome ? q() : ' not',
      " a palindrome!!!\n";
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