Currently we can't get it.
I tried with any other apis, I did not find a way.
Thanks a lot for the effort! Appreciated!
The only workaround I have found is to manually go and check the lead activity log for the "Add to Engagement Program". This gives information on both the stream id and stream name, so they can be matched.
It requires some manual effort though depending on the number of programs/streams. Looking forward to have this information available via the api in the future.