My simple html php form not inserting into database

For some reason, this form doesn't insert into my database.

Html

<form action="../php/register.php" method="post">
    <div id ="personal-form">
        <h4><b>Personal Details:</b></h4>
        <hr>

        <div class="form-group">
            <label class="sr-only" for="first-name">First name</label>
            First Name

            <input type="text" name="firstname" placeholder="" 
                   class="form-control" id="firstname">

            <button type="submit" class="btn btn-next" id="submit">
                Submit
            </button>
        </center>
        </div>
    </div>
</form>

php/register.php

<?php
    include('connect.php');

    if(isset($_POST["submit"])) {
        $firstname = $_POST["firstname"];
        $stmt = $conn->prepare("INSERT INTO storeowners (firstname) VALUES 
(:firstname)");

        $stmt->bindParam(':firstname', $firstname);
        $stmt->execute();

        header("location: next.php");
    }
?>

This is connect.php

<?php
    $servername = "localhost";
    $username = "root";
    $password = "";

    try {
        $conn = new PDO("mysql:host=$servername;dbname=blaza", $username, 
$password);
        //set the PDO error mode to exception
        $conn->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
        echo "success";
    } catch(PDOException $e) {
        echo "Connection failed: " . $e->getMessage();
    }
?>

When I click on submit button, it shows the php/register.php page with the message success which is thesame message in the connect.php code if db connection was successful. I dont know where the problem is cause it doesnt store the firstname to the database and no error was given.