Where are you trying to delete the "document name" from? And in what version
of Word?
If what you're saying is that you have deleted the file but it still shows
up on the File menu or in the Getting Started task pane, and if this is Word
2003 or earlier, then it can be removed. Press Ctrl+Alt+Hyphen (the mouse
pointer will change to what I like to think of as a large minus sign) and
then mouse over the File menu to open it. Click on the filename you want to
remove.
Be very careful with this pointer because it will remove any menu item you
click on. It is "used up" after one use, however, and if you ever enable
this function inadvertently, you can dismiss it with ESC.
Removing the filename from the MRU list at the bottom of the File menu also
removes it from the task pane. If you have Word 2007 and want to remove a
specific file from the Office Button menu, this is less straightforward. See
http://gregmaxey.mvps.org/Recent_Files_List_Editor.htm