If I get you right, it's as simple as this:

my @unsorted =
(
    {
        'is_selected' => 1,
        'name' => 'Me',
        'user_id' => '1'
        },
    {
        'is_selected' => 0,
        'name' => 'Admin Admin',
        'user_id' => '14'
        },
    {
        'is_selected' => 0,
        'name' => 'Proximate Shine',
        'user_id' => '15'
        }
);

my @sorted = sort { $a->{name} cmp $b->{name} } @unsorted;

print join "-", map { $_->{name} } @sorted; #Admin Admin-Me-Proximate 
+Shine
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