It is possible to do it using VBA.
First Enter the below formula into
CELL A1, this can be changed to any cell you want, just ensure you change the reference point in the macro part.
It will create your dynamic date and sheet name combo.
Then put the below into a module:
Private Sub Workbook_BeforePrint(Cancel As Boolean)
ActiveSheet.PageSetup.CenterHeader = Range("A1").Value
It will take the date combo and set it into your header before printing.
It should also come into effect before you view the print preview.