How to send email with wp_mail() with from email taken from contact form instead of the host?

You don’t need to pass the from name and email to PHPMailer in your code as it will take it from $headers so try the following:

add_action( "phpmailer_init", "send_smtp_email" );
function send_smtp_email( $phpmailer ) {
// ini_set("sendmail_from","[email protected]");
// ini_set("sendmail_path","[email protected]");
    // Define that we are sending with SMTP
    $phpmailer->isSMTP();
    // The hostname of the mail server
    $phpmailer->Host = "localhost";
    // Use SMTP authentication (true|false)
    $phpmailer->SMTPAuth = false;
    // SMTP port number - likely to be 25, 465 or 587
    $phpmailer->Port = "25";
    // Encryption system to use - ssl or tls
    $phpmailer->SMTPSecure = "tls";

    // $phpmailer->From = "[email protected]";
    // $phpmailer->FromName = "XYZ";
    }

Also, double check the form field name for: $_POST['namee']