First:
Cookies must be sent before any other headers are sent.
index.php
---- CODE ----
<?
$User = "Felipe";
setcookie ("Name", "$User", time() + 3600);
//3600 seconds = 1 hour
?>
<body>
.<br>
HI<br>
.<br>
</body>
---- CODE ----
Test.php
---- CODE ----
<?
if (isset($User)){
print "OK";
} else {
print "Not";
}?>