The active license can be observed in the Help | Register dialog or Register link at the bottom of the product Welcome Screen (when there is no project open).
License itself is stored in the <product><version>.key file under the IDE configuration directory.
When using JetBrains Account or the new offline activation key, information is encrypted and is stored in the system registry, therefore there is no way to access it for the end user.
Please note that this file has UCS2 (2-byte Unicode) encoding and you can't view it in basic editors like Notepad, you need to open it in some Unicode-aware editor if you goal is to find the user name and the key. First line contains the key, second line contains user name.