Янковиц,
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
</head>
<body>
<div class="one-one">
<div class="menu-name">Пункт 1</div>
</div>
<div class="two-two">
<div class="menu-name">Пункт 2</div>
</div>
<div class="three-three">
<div class="menu-name">Пункт 3</div>
</div>
<script type="text/javascript">
newtext='<span>new</span>';
document.getElementsByClassName("two-two")[0].getElementsByClassName("menu-name")[0].innerHTML = 'Пункт 2 ' + newtext;
</script>
</body>
</html>