To name the log based on your scenario you will have to create an external script, maybe you can even copy the log in a more convenient location. The MSI Command Line field from the Bootstrapper Options only allows pseudo-formatted properties reference. At build time the property references are replaced with the value of the respective properties.

For example, you can take advantage of the MsiLogging property. Windows Installer will automatically set the MsiLogFileLocation property to the full path of the log file. In order to generate an installation log, you can check the Enable Verbose Logging option from the Install Parameters view. By enabling this option, a log file will be generated each time the install package runs.

Then, you can have a custom action at the end of the installation that will copy & rename the log to the desired location and preferred naming convention.

You may need to add a few seconds of delay when your script is running, to give enough time for the log to have all the windows-installer events. After this, you can execute the custom action.

There are a few threads on the Advanced Installer forums explaining how to integrate the custom action, check the Possible to copy the verbose log after install to AppDir for more details.

Let me know if you need any help to sort this out.