Welcome to the Wefugees Community and thank you for your question.
I think in this matter you need to differentiate between a situation where you are still in the asylum procedure and a successfully completed asylum process. If the Greek authorites' decision on your asylum application is still pending, I am quite sure that they will not allow you to travel to another country. In the case you hold a residence permit already and a valid travel document as well, you can travel within the Schengen area for up to 90 days.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,