Why is $name field never !, even when empty?

I have a basic sign up form, and when checking if a field is not set (if(!$name)) it always goes to 'else', even when the field is empty. Does anyone know why? (When i'm trying to check it in reverse (if($name)), it does show the error line. )

Thanks a lot!

<?php
$error = '';
if(isset($_POST['submit'])){

$name = trim(filter_input(INPUT_POST, 'name', FILTER_SANITIZE_STRING));

  if( !$name && preg_match("/^([\w]){2,50}$/", $name)){ 

    $error = ' * Please enter a valid name';

}

?>

 <form action="" method="post">

            <label for="name">Name:</label><br>
            <input type="text" name="name">   <br><br>
<input type="submit" name="submit" value="Sign up">
            <span class="error"><?= $error ?></span>
</form>