Not under strict.pm! You are actually accessing global package variables when you open on a string like that. If you want to make this work, you need to store the filehandles somewhere like this (5.6 on up) example:

my %hash = (
  one => "first bit",
  two => "second bit",
);

my %fh;
foreach my $file_name (keys %hash) {
  open (my $fh, ">", $file_name)
    or die "Could not write to '$file_name': $!";
  $fh{$file_name} = $fh;
}

foreach my $key (keys %hash) {
   print {$fh{$key}} "$key => $hash{$key}\n";
}
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Of course if you've gone this far, then you may want a mapping between keys and file names...