According to Alex's answer above, recipients will know the first person in the list even if you're using BCC. A solution for this would be to send individual copies to each address one by one.
$emails = ['a@example.com', 'b@example.com', 'c@example.com'];
foreach ($emails as $email){ // or $result as $row
mail(
$email, // or $row['address']
'Same Subject',
'Same Content',
'From: same_sender@example.com',
'-f same_sender@example.com'
);
}