Have a look at the helper class: Mage_Customer_Helper_Data
To simply get the customer name, you can write the following code:-
$customerName = Mage::helper('customer')->getCustomerName();
For more information about the customer's entity id, website id, email, etc. you can use getCustomer function. The following code shows what you can get from it:-
echo "<pre>"; print_r(Mage::helper('customer')->getCustomer()->getData()); echo "</pre>";
From the helper class, you can also get information about customer login url, register url, logout url, etc.
From the isLoggedIn function in the helper class, you can also check whether a customer is logged in or not.