Comments are in. Hope you find them helpful in pointing me in the right direction. I tested the 2 argument bless in the first subroutine. When it was data dumped, I didn't see any change in how the data was stored.

I went with the first one since it is the most straight forward. It does not have any of my other custom subroutines used in it and stands on its own.

sub accounts {
  my ($class) = @_;
  
  my @accounts = qw(
    Lady_Aleena
    LadyAleena_ABC
    LadyAleena_CBS
    LadyAleena_FOX
    LadyAleena_NBC
    LadyAleena_SyFy
    LadyAleena_TNT
    LadyAleena_USA
    LadyAleena_TV
    LadyAleena_eros
    LadyAleena_home
    LadyAleena_test
  );
  
  return bless \@accounts, $class;
}
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After adding $class on the last line, the data dumped looked like...

$VAR1 = bless( [
                 'Lady_Aleena',
                 'LadyAleena_ABC',
                 'LadyAleena_CBS',
                 'LadyAleena_FOX',
                 'LadyAleena_NBC',
                 'LadyAleena_SyFy',
                 'LadyAleena_TNT',
                 'LadyAleena_USA',
                 'LadyAleena_TV',
                 'LadyAleena_eros',
                 'LadyAleena_home',
                 'LadyAleena_test'
               ], 'Twitter::Objects' );
[download]

I got the same result without $class on the last line. When I use the subroutine as an object, I would do something like...

use strict;
use warnings;

use lib '../files/perl/lib';
use Twitter::Objects;

my $accounts = Twitter::Objects->accounts;

for my $account (@{$accounts}) {
  print $account;
# and other code I want to run through this loop.
}
[download]

I'm not sure what I'm missing.