This is currently not supported on the CSC module itself - it will only log denied flows.
There are a number of options available to determine what IP addresses access devices outside the ASA. You can monitor the connection syslogs - this will not provide the hostname on the outside but will provide the inside IP address, the translation, and destination IP address. If you enable 'inspect http', this command will create a syslog with each URL access (however, enabling this feature may have adverse effects on some websites). Implementing NetFlow (available in ASA version 8.2) will give you the ability to more easily watch flows.