I have just put a new pre-release online which updates the utility
Export » Export selection or active sheet as new file....

The default proposed filename now contains the name of your workbook and the selected sheet. If you have chosen to export a range of cells instead of the entire sheet, the proposed filename also contains the address of your selection:

Download

Download via the ASAP Utilities FAQ
//www.asap-utilities.com/faq-questions-answers-detail.php?m=155