To remove the name properly, you need to find the MRU in the Registry and
delete it. You may need to rename other MRU entries so that the MRU numbers
as consecutive.
You can find these MRU entries in the Registry branch:
HKCU\Software\Microsoft\Office\10.0\Access\Settings
if you use A2002. If you use one of the other versions, look for equivalent
Registry branch.
Personally, I never worried about the MRU pointing to a deleted database.