Alternative to php echo within code

I can't speak to how the above code is actually implemented, but the very first part is a misuse of "echo." Everything under "" should be outside of of it.

How exactly you handle the rest of the code (and whether it makes sense) is impossible for me to say, but you might see something like (I'd probably not write it this way, but whatever...):

function add_content2() {   

    // CONNECTS TO DATABASE
    $dbtype = mysqli_connect("localhost", "JohnLyons", "2012Zombies123!", "b1s243006078611");

    if( ! $dbtype ) {
    die(mysqli_error($dbtype));
    }

    // WHAT HAPPENS ON SUBMIT
    if(isset($_POST["submit"])) {
        $name = $_POST["name"];
        if(empty($name)) {
            wc_add_notice(("Fill in the entire field"), "error");
        } else {
        // Queries database. How to get header to stay on page
            mysqli_query($dbtype, "INSERT INTO todo(name) VALUES ("$name")");
            $referer = $_SERVER["HTTP_REFERER"]; 
            header("location: $referer");
        }
    }

    $name_loop = mysqli_query($db, "SELECT * FROM todo"); 

    //END FIRST LINES - maybe something more/else goes here or even is in a separate function or file?   

    echo '<tbody>' ;

    while ($row = mysqli_fetch_array($name_loop)) { 

        echo '<tr>
                <td>' . $row["name"] . '</td>
            </tr>' ;
                
    }   
    
    echo '</tbody> ' 

    echo '<form style="padding-top: 30px" method= "' . $_SERVER["PHP_SELF"]; . ' >' ;

    if (isset($error)) { 
        echo '<p>' . $error . '</p>' ;  
    } 

    echo '<input type="text" placeholder="Enter student information" name="task">' ;

    echo '<button type="submit" name="submit" style="margin-top: 10px">Register Student</button>' ;

    echo '</form>' ;
    
}

PHP has the <?= shortcut that I find a bit more legible, especially when used in conjunction with PHP Braceless syntax.

/* First let's exit PHP mode */ 
?>
<tbody>
  <?php while ($row = mysqli_fetch_array($name_loop)): ?>
  <tr>
    <td><?= $row["name"] ?></td>
  </tr>
  <?php endwhile ?>          
</tbody>

<form style="padding-top: 30px" method= "<?= $_SERVER["PHP_SELF"] ?>" >
  <?php if (isset($error)): ?>
   <p><?= $error ?></p>
  <?php endif ?>
  <input type="text" placeholder="Enter student information" name="task">
  <button type="submit" name="submit" style="margin-top: 10px">Register Student</button>
</form>

<?php /* this returns us to php mode. */

Personally, I go a step further and use the Timber library which bridges into the Twig template engine. This is what the code above looks like in Twig

<tbody>
  {% for row in rows %}
  <tr>
    <td>{{ row.name }}</td>
  </tr>
  {% endfor %}          
</tbody>

<form style="padding-top: 30px" method= "<?= $_SERVER["PHP_SELF"] ?>" >
  {% if error %>
   <p>{{ error }}</p>
  {% endif %>
  <input type="text" placeholder="Enter student information" name="task">
  <button type="submit" name="submit" style="margin-top: 10px">Register Student</button>
</form>

Of course, to use the template, you have to load your data into it which is beyond the scope of this response. If the above looks interesting the project guide is here: https://timber.github.io/docs/v2/

P.S. There is no reason to use the mysqli functions directly in a WordPress application. I strongly advise you use the $wpdb connector object or, even better, the WP_Query class to work with the database.