Questo non l'ho provato. Facci sapere…:

codice:
<!doctype html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>Esempio</title>
<script type="text/javascript">
function updateLabel () {
	document.querySelector("label[for=\"browseFile\"]").innerHTML = this.value;
}
</script>

</head>
<body>

<form method="post" action="invia.php" name="tuoForm">
	


		File:
		<input name="tuoFile" type="file" id="browseFile" onchange="updateLabel.call(this);" style="display:none;">
		<label for="browseFile" style="cursor:pointer;">Scegli file</label>
	</p>
</form>

</body>
</html>