Try this in your local.xml
<?xml version="1.0"?>
<layout version="0.1.0">
<default>
<reference name="top.links">
<!-- Remove cart, checkout and wishlist top links -->
<remove name="checkout_cart_link" />
<remove name="wishlist_link" />
<!-- Remove my account top links -->
<action method="removeLinkByUrl"><url helper="customer/getAccountUrl"/></action>
</reference>
</default>
<!-- getting rid of login logout links in top .links -->
<customer_logged_in>
<reference name="top.links">
<action method="removeLinkByUrl"><url helper="customer/getLogoutUrl"/></action>
</reference>
</customer_logged_in>
<customer_logged_out>
<reference name="top.links">
<action method="removeLinkByUrl"><url helper="customer/getLoginUrl"/></action>
</reference>
</customer_logged_out>
</layout>
In your phtml use this
<ul>
<li>
<?php if(Mage::getSingleton('customer/session')->isLoggedIn()){ ?>
<?php
$customer = Mage::getSingleton('customer/session')->getCustomer();
$cusname = $customer->getFirstname().' '.$customer->getLastname();
$name = substr($cusname,0,18)."..";
?>
<a href="<?php echo Mage::getUrl('checkout/cart'); ?>"><?php echo "Hi "."$name" ?> </a>
<ul class="subaccount">
<li><a href="<?php echo Mage::getUrl('customer/account'); ?>">Profile</a></li>
<li><a href="<?php echo Mage::getUrl('sales/order/history'); ?>">Order</a></li>
<li><a href="<?php echo Mage::getUrl('wishlist'); ?>">Wishlist</a></li>
<li><a href="<?php echo Mage::getUrl('newsletter/manage'); ?>">Newsletter</a></li>
<li><a href="<?php echo Mage::getUrl('review/customer'); ?>">Review</a></li>
<li><a href="<?php echo Mage::getUrl('customer/account/logout'); ?>">Logout</a></li>
</ul>
<?php } else { ?>
<a href="<?php echo Mage::getUrl('customer/account/login'); ?>">Login / Register</a>
<?php } ?>
</li>
</ul>