<html>
<head>
</head>
<body>
<script>
var a = prompt("Ваше имя?");
localStorage.setItem('userName', a);
if(document.location.pathname != '/index.html') top.location = 'index.html';
</script>
</body>
</html>
index
<html>
<head>
</head>
<body>
<script>
if(localStorage.getItem('userName')=="null"||localStorage.getItem('userName')=="") document.write('Дорогой друг');
else document.write('Дорогой '+localStorage.getItem('userName'));
</script>
</body>
</html>