By default the conversation header of an entity record (case) shows the WQ, the work stream, the "case subjet", the date when the item was picked and the conversation "status reason".
It would be nice to be able to provide more information on the header such as "case number" and "customer".
Needs Votes
Ideas Administrator

The number of fields displayed in the Conversation header is fixed at 4. One option is to remove one of the existing fields from the Conversation header/ move it to the Details or Footer section and add Customer field. It's possible today to add Case Title as well but not Case number.

Our product management team is reviewing these suggestions. Please continue to add comments and discuss use cases on this thread to help us understand your needs!