Anonymous Monk,
Updated to reflect your updated requirements:
You havent said how big your file is but let us assume you have enough resources to store the whole file in memory.

my $log_file = $ARGV[0] || 'log.file';
open(my $fh, '<', $log_file) or die "Unable to open '$log_file' for re
+ading: $!";
my %name;
while (<$fh>) {
    chomp;
    my ($fn, $ln, $rest) = $_ =~ /^(\w+)\s+(\w+)(.*)/;
    $name{$ln} = "$ln $fn$rest\n";
}
for (sort keys %name) {
    print "$name{$_}";
}
[download]

It does assume last names are unique. If this is not the case, you could always use a two level hash $name{$ln}{$fn} and if that still is not unique you could use $rest as in $name{$ln}{$fn}{$rest}.