When I originally signed up with Dropbox my machine was called one thing (Dragon). But, it was renamed along the way (Lion). However, when I log into my admin account, and selected Security--->Devices it still says my computer is named Dragon; and properly reflects that there's been activity within the last hour.
Your system should be able to detect name changes without my having to log out of the Dropbox application on my computer, and then log back in; forcing a reindexing. We currently have 2Tb+ of files; which is probably 1,000,000 or more files. The help desk suggested pairing that down to 300,000, OR LESS files. That is NOT going to happen.