The first example was bare as possible to show the basic principle. In practice logs have lots of redundancy so you should cache and handle lookup errors. If this was run for a very long time or a super busy site you'd clear the cache once in a while too (with Vins reminder that gethostbyaddr is obsolete (and slow)):

use strict;
use feature qw(say);
use Socket;
use File::Tail;

my $file = File::Tail->new("/some/log/file");
my $seen = {};
my $line;

while (defined($line = $file->read)) {
    if ($line =~ /^DATE (IP) (WHATEVER)/) {
       my $remote_ip   = $1;
       my $whatever    = $2;
       my $remote_host;

       if ($seen->{$remote_ip}) {
           $remote_host = $seen->{$remote_ip};
       else {
           $remote_host = getaddrinfo(inet_pton($remote_ip),AF_INET) |
+| 'none';
           $seen->{$remote_ip} = $remote_host;
       }
       say join "\t", qw/$remote_ip $remote_host $whatever/;
    }
}
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