I have the same issue. I know how to reproduce the problem, just not a fix or a work around.
When you edit a contact in the native Android contact application, it changes the "file as" name to First Name Last Name. This happens behind the scenes and I cannot find out how to prevent this.
Touchdown reads the Exchange servers "file as" name. If you log into your Outlook Web Access and view the "file as" in list view, the names of people you edited in the native contact app will also be listed as first name last.
Whats funny is that in Outlook, if you open the contact the "file as" is listed correctly (i.e. Last name, First name), BUT if you go to list view and add the "File as" column you will see that the contact "file as" is really listed First Name Last Name. Not sure why they show differently.
To correct the contact, go into Outlook, change the "File as" to another selection (i.e. first name last name), save the contact, then change the "file as" back to Last Name, First Name and save again. (You can also do this in Outlook Web Access to correct the name formatting).
When the contact syncs again with Touchdown it will be displayed correctly. (also displayed correctly on Outlook Web Access).
If you edit the contact in Touchdown, there is NO problem, it saves fine. I only have the problem if I edit the contact in the native contact app.
I have done a LOT of searching on this topic. Seems like there were several posts about the issue in 2009, no one posted any fixes. So I assume people just live with the issue. Most people probably don't even know the problem exists, because the Native contact app and Outlook appear to list them correctly.
From my research, it appears the native contact app, sends the "Full Name" out to the server, which gets saved as the "File As" name. (BTW Full Name is typically formatted like First Name Last Name). But since Activesync has no options for field mapping. I don't think there is anything we can do.
I have tried many different scenarios. The issue has nothing to do with Outlook on your computer, because, i have tested making changes while Outlook was offline, and the issue still happens.
FYI, I have a Samsung Galaxy Nexus, Outlook 2010, Exchange Server 2003, and I also use Touchdown.
Anyone have any insight they would like to share?