Use a hash instead:

#!/usr/bin/perl
use warnings;
use strict;

my %booksByBorrower = (
    adam => {"Learning Perl" => {borrowed => '2015-12-17'}},
    jake => {"Programming Perl" => {borrowed => '2015-12-08'}},
    john => {"Programming Perl" => {borrowed => '2015-12-12'}},
    betty => {"High Order Perl" => {borrowed => '2015-12-10'}},
);

for my $name (sort keys %booksByBorrower) {
    print "$name\n";
    
    for my $book (sort keys %{$booksByBorrower{$name}}) {
        print "  Borrowed $book $booksByBorrower{$name}{$book}{borrowe
+d}\n";
    }
}
[download]

Prints:

adam
  Borrowed Learning Perl 2015-12-17
betty
  Borrowed High Order Perl 2015-12-10
jake
  Borrowed Programming Perl 2015-12-08
john
  Borrowed Programming Perl 2015-12-12
[download]

Of course for this sort of task you should really be using a database, but that's a little heavy for such a trivial example.