Not in the submit event handler itself, no.
But what you can do is add click handlers to each submit which will inform the submit handler as to which was clicked.
Here's a full example (using jQuery for brevity)
<html>
<head>
<title>Test Page</title>
<script src="http://code.jquery.com/jquery-latest.js"></script>
<script type="text/javascript">
jQuery(function($) {
var submitActor = null;
var $form = $('#test');
var $submitActors = $form.find('input[type=submit]');
$form.submit(function(event) {
if (null === submitActor) {
// If no actor is explicitly clicked, the browser will
// automatically choose the first in source-order
// so we do the same here
submitActor = $submitActors[0];
}
console.log(submitActor.name);
// alert(submitActor.name);
return false;
});
$submitActors.click(function(event) {
submitActor = this;
});
});
</script>
</head>
<body>
<form id="test">
<input type="text" />
<input type="submit" name="save" value="Save" />
<input type="submit" name="saveAndAdd" value="Save and add another" />
</form>
</body>
</html>