对于所选的每个表单选项，添加到mysql

I have a multiple select form:

<form method="post" action="register_results.php" name="registerform" class="form-horizontal" role="form">

    <div class="label">Select Name:</div>
    <select name="names" multiple="yes" size="15">
    <option value = "">---Select---</option>
    <?php
    while ( $row=mysqli_fetch_assoc($result)) {
      echo "<option value='".$row['registrant_name']."'>".$row['registrant_name']."</option>";
    }
    mysqli_close($con);
    ?>
    </select>  
</form>

The register_results.php file looks like this:

$registrant_name = $_POST['names'];
$event_result = $_POST['result'];


$query = "UPDATE events_regged SET result = $event_result WHERE event_name='event10' AND registrant_name=('$registrant_name') ";
$result = mysqli_query($con, $query);

I want to be able to add multiple mysql rows (one row for each username) if multiple names are selected in the form. How can I do that?

Use

<select name="names[]" multiple="yes" size="15">

instead of

<select name="names" multiple="yes" size="15">

and use foreach

foreach($_POST['names'] as $value)
{
//your query goes here
}

Change the form select element name from "names" to "names[]" and then you can access an array of posted values - which you can then iterate through.

You have some changes required within your code as

<select name="names" multiple="yes" size="15">
              ^^^^^

it should be

<select name="names[]" multiple size="15">

This will result into an array so the result of

$registrant_name = $_POST['names']

will be an array

First change your form as below (it's more elegant and fast to use Id instead of name (string) in Sql):

<select name="ids[]" multiple size="15">
    <option value = "">---Select---</option>
     <?php
       while ( $row=mysqli_fetch_assoc($result)) {
      echo "<option value='".$row['registrant_id']."'>".$row['registrant_name']."</option>";
}
     mysqli_close($con);
?>
</select> 

And in your PHP use foreach:

 $registrant_ids = $_POST['ids'];
 $event_result = $_POST['result'];
 foreach($registrant_ids as $id)
   {
     $query = "UPDATE events_regged SET result = $event_result WHERE event_name='event10' AND registrant_id=".$id;
     $result = mysqli_query($con, $query);
   }