Your code should not have major PHP configurations or initializations like this. I  does not look smart. Tidy it up.
<select size="1" name="domeinnaam"> 
  <?php 
  include '../config.php';
  $sql = "SELECT * FROM megabase";  
  $resultaat = mysql_query($sql) or die (mysql_error());  
  while ($row = mysql_fetch_array($resultaat))       
  { 
  echo '<option>' . $row['domeinnaam1'] . '</option>';
  }
  ?>
 </select>
  <?php 
  include '../config.php';
  $sql = "SELECT * FROM megabase";  
  $resultaat = mysqli_query($conn, $sql) or die ($conn->mysqli_error());  
  ?>
<select size="1" name="domeinnaam">
<?php
while ($row = mysqli_fetch_array($conn, $resultaat))       
      { 
      echo '<option>' . $row['domeinnaam1'] . '</option>';
      }
?>
 </select>
Next don't really try to break options, you could use javascript frameworks like JQuery to achieve a more stylish select. I don't really think you can do this:
while ($row = mysqli_fetch_array($conn, $resultaat))       
  { 
  echo '<option>' . $row['domeinnaam1'] . '<br />' .$row['domeinnaam2']. '</option>';
  }
Using JQuery, you could a list item in a div:
<ul>
while ($row = mysqli_fetch_array($conn, $resultaat))       
      { 
      echo '<li>' . $row['domeinnaam1'] . '<br />' .$row['domeinnaam2']. '</li>';
      }
</ul>
Then pass the selected item to a hidden field for later use using the onclick event. 
If you want to display the 10 columns in one loop as separate options, this could do it.
while ($row = mysqli_fetch_array($conn, $resultaat))       
{ 
echo '<option>' . $row['domeinnaam1'] .'</option>';
echo '<option>' . $row['domeinnaam2'] .'</option>';
echo '<option>' . $row['domeinnaam3'] .'</option>';
echo '<option>' . $row['domeinnaam4'] .'</option>';
echo '<option>' . $row['domeinnaam5'] .'</option>';
echo '<option>' . $row['domeinnaam6'] .'</option>';
echo '<option>' . $row['domeinnaam7'] .'</option>';
echo '<option>' . $row['domeinnaam8'] .'</option>';
echo '<option>' . $row['domeinnaam9'] .'</option>';
echo '<option>' . $row['domeinnaam10'] .'</option>';
}
I wonder where this would be useful and how. Anything can happen in programming.  :)