my @all_names = map { {name => $_->{name}} } @{ $data }[1 .. $#$data];
[download]

use warnings;
use strict;
use Data::Dumper;

my $data = 
[
  {
    val => "action",
    name => "Accounts",
    id => "None",
  },
  { name => "PA1", id => "AUTOB" },
  { name => "PB3", id => "AUTOP" },
  { name => "BOX", id => "BOP" },
  { name => "DW0", id => "DFIRE" },
  { name => "QW3", id => "HOME" },
  { name => "CM7", id => "CUMBR" },
  { name => "BR1", id => "PUMBR" },
  { name => "TY6", id => "ECUST" },
]
;

#my @all_names = map { $_->{name} } @{ $data }[1 .. $#$data];
#my @hash_names = map{ {name=>$_} } $data;
my @all_names = map { {name => $_->{name}} } @{ $data }[1 .. $#$data];

print Dumper(\@all_names);
#print Dumper \@hash_names;

__END__
[download]

why wouldn't the name=>"Accounts" be picked up

Because you start at element #1, not 0:

[1 .. $#$data];
 ^
 |
 |
 Here!
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($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]

why wouldn't the name=>"Accounts" be picked up

In your original data the first element of the array is unwanted so toolic has @{ $data }[1 .. $#$data] which has the effect of skipping that first element. Arrays are indexed from "0" so the first element is $array[0], the second element is $array[1] and so on. So, @{ $data }[1 .. $#$data] means the range of elements starting at the second element and up to the last element.

A better way might be to use grep in combination with map:

my @all_names =
    map { {name => $_->{name}} }
    grep { exists $_->{name} }
    @$data;
[download]

Here grep first filters all the elements, discarding any which don't have a 'name' key, and then map constructs the desired data structure from the remaining elements.