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">
var newtext=' <span>new</span>';
document.querySelector('.two-two .menu-name').insertAdjacentHTML('beforeEnd', newtext)
</script>
</body>
</html>