HTML Forms - Are name and id required?

name is used by the server-side. This is necessary if you plan to process the field. id is only so label elements, when clicked and accessed by screen-readers, can trigger/invoke the form controls (inputs and selects).

<form method=POST action="form-processor.php">
    <input name=first_name value=john>
</form>

results in

$_POST = array('first_name' => 'john');

If the method is GET, it's appended to the query string:

http://site-name.com/form-handler.php?first_name=john

It's popular for query string appending with hidden inputs:

<input type="hidden" name="q" value="1">

name is needed for POST and GET... but not id... id is used for client-side processing.