If you SaveAs a document with the choice of filename you want to use, then the PDF would adopt that name. However this is likely to give you a second copy of the original file that you might then wish to delete.
I recently created
http://www.gmayor.com/email_document.html which is essentially an alternative to save and send, albeit using a slightly different process which includes the default signature for the e-mail account. It might make an interesting update project to provide an option to choose or change the filename of the attachment. What did you have in mind?
P.S. I liked the idea of renaming the attachment, so have implemented it at the above link.