Single "Chrome" Device

I use Join on Chrome via my university remote Windows server. The server is setup such that all data is wiped after each logoff. This causes Join to register a new Chrome device for every time I login to the remote server. For example, after 3 individual logins the Join device list contains 3 Chrome "devices", but the first two no longer exist.

Is there a way to combine all Chrome logins as one device within Join? As an example, with ChromeIPass, it prompts the user to give a device name, and if it matches an existing device, it prompts to overwrite.