Почему?
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script>
$(function() {
$(".bbQuoteName").click(function(){
alert($(this).next().text())
})
});
</script>
</head>
<body>
<div class="bbQuoteName">Блок 1</div><div class="quoteMessage">Текст 1</div>
<div class="bbQuoteName">Блок 2</div><div class="quoteMessage">Текст 3</div>
</body>
</html>