From the Access 2003 menu, File -> Database Properties brings up a tabbed dialog which includes a Statistics tab with a line labelled "Last saved by:". However, I checked several of my databases, and none of them have an entry after that label. The dialog does not allow me to type in anything either. And I can't find any programmable method to set or retrieve a value for last saved by. I couldn't turn up any additional information from web searches.
Perhaps that property is unused. I don't know.
I'm also curious what it would mean for an Access database. At first blush, I would think it should mean the last user to insert, update, or delete table data. However the disk file can be updated for any of a number of other reasons: changes to forms or reports; adding or dropping an index; even simply running Compact & Repair without changing any data.
I think you would have to design your own provision to keep track of which user last modified table data. Allen Browne has an article, Creating an Audit Log, which might help you do the tracking you want.