You can get the name of the currently playing asset a few ways. The dead simplest way, if you don’t mind sorting through some logging information, would be to set FMOD for Unity’s logging level to “Log”, which will log information on the created sound, including the asset name.
A more sophisticated solution is to use an event callback on sound creation to get the name of the sound. You can see how to do so in Connor’s reply to a similar question here: