If your application process authentication using IAM or another Google API, you can utilize audit logs. Most chances the call to authentication API will be logged as part of the system or admin audit log. You may need to enable data read logs to have this audit logging (which will incur cost of storing the logs).

If you do not do it or, you want this info to be a part of each log entry that you write within the request processing, you will have to implement it using your logging framework of choice. You can store it as a user label.