A little recursive sub to compile this into the right format:

use strict;
use warnings;

use Data::Dumper qw( Dumper );

my %tree;

while (<DATA>) {
   chomp;
   my $p = \%tree;
   foreach (split(qr{\s*/\s*}, $_)) {
      $p = $p->{$_} ||= {};
   }
}

sub re_format {
    my $data = shift;
    my $out = [];
    for my $key (keys %$data) {
        my $temp = { name => $key};
        if (keys %{ $data->{$key} }) {
           $temp->{children} = re_format($data->{$key})
        }
        push @$out, $temp;
    }
    return $out;
}    

print Dumper('First Step' => \%tree, 'Final' => re_format(\%tree));

__DATA__
one
foo / bar
foo / baz
foo / qux / two
foo / qux / three
foo / qux / four
five
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