Hello,
it is possible to see a FME workspace CPU usage at the end of a job in the logging.
However, when you activate a stream it will occupy an Engine and it will not give CPU usage in the logging.
Is there a way to find or register the CPU usage of a stream that runs 24/7?
Hello,
The completed jobs web page can be filtered by source type " Streams" and that could be a good indicator of CPU Usage by the engine assigned to the stream. reference- https://community.safe.com/s/article/How-to-Use-the-FME-Server-Streams-Interface ]. If this does not satisfy your requirements, please feel free to submit an idea to add this as a feature. 
There is a CPU/memory footprint for an FME Engines process, including if it is idle but we do not track/provide that. No usage-based credits will be used for an idle FME Engine that isn’t running a job.
Thank you for the quick response. The problem is that it does not display any CPU usage when the stream is running. If I cancel the stream after receiving several messages I also don't see any CPU usage. 
Hi @bryanmayor ,
Job statistics are not currently available for Streams, as it relies on translation completion. However, I filed the request with our development team for this functionality (internal reference FMEFLOW-21844). I recommend filing an idea on the community so that others can vote on it! Hope that helps.