For PostBack updates, you can place a label control above the calendar and set its text from code behind based on DayPilotMonth.StartDate value.
If you change the date using a callback, you can use AfterRenderJavaScript
to change the value on the client side. Something like this:
AfterRenderJavaScript="document.getElementById('monthLabel').innerText = dp.startDate.toString('MMMM yyyy');"