$query = "UPDATE `pokemon_user` SET `name`= '{$_POST[name]}' WHERE `id`={$_POST[id]} AND `user`='{$_SESSION[id]}';";

<?php
if (isset($_POST['name_pokemon']) || isset($_SESSION['id'])) {
$query = "UPDATE `pokemon_user` SET `name`= '$_POST['name_pokemon']}' WHERE `user`='{$_SESSION['id']}';";
$result = mysql_query($query) or die("Неизвестная ошибка!");
echo "<script>alert('Вы удачно сменили имя !');</script>";   
} else {
echo"<script>alert('bla... bla.. bla...');</script>";
}
?>
<?php
/* .... */    
?>
<form method=POST>
<input type=text name=name_pokemon maxlength=20 style=width:12%>
<input type=submit value=OK>
<input type="reset"  title="Очистить поля" value="X">
</form>