If their middle names are different and if you have access to site settings, you might try changing the Full name format under Administration > Users > Permissions > User policies, so that instead of the default setting, language, you use firstname middlename lastname. This will add their middlenames as part of the file download. You could also try firstname alternatename lastname and make sure they put something different into the alternate name field of their profiles. You can also try other combinations of name settings listed in the directions for Full name format. and Alternative full name format.
Currently, in my 3.0.4+ site, I am using firstname "alternatename" lastname. I have students put their nickname in the Alternate name field of the General section of their profiles. It shows up everywhere in Moodle with the quote marks around it, but the quote marks are stripped out when I download files for grading. I tell them at the start of the year to be "Clean" with what they put there, and that I reserve the right to change any inappropriate entry. This gives them the opportunity to have me call them whatever they are normally known as, in case they don't go by their normal first name. e.g. "Bob" instead of Robert.