Assuming the app has access to the name of the application that is playing music when submitting a listen, that name can be added to the listen metadata:

As per https://listenbrainz.readthedocs.io/en/latest/users/json.html#payload-json-details
we can put it under the following path:

track_metadata.additional_info.media_player

and if we have version information: track_metadata.additional_info.media_player_version