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my $first = 1;
for my $n (sort { $hash{$a} <=> $hash{$b} } keys %hash){
...

   ...
}

my @names_by_val = sort { $hash{$a} <=> $hash{$b} } keys %hash;
shift(@names_by_val);
for my $n (@names_by_val) {
   ...
}

my @names_by_val = sort { $hash{$a} <=> $hash{$b} } keys %hash;
for my $n (@names_by_val[1..$#names]) {
   ...
}

my %hash;
foreach my $n (@names){
...
    $hash{$n}=$r;
}
my @names_by_val = sort { $hash{$a} <=> $hash{$b} } keys %hash;

use List::Util qw( shuffle );
my @shuffled_names = shuffle @names;