This issue is not specific to DisplayLink and is an underlying bug with Windows. There is a thread on the Microsoft forum about this issue here: Windows 7 IT Pro > Windows 7 User Interface > Changing monitor identities?
It may be possible to work around this by forcing Windows to re-detect monitors:
How to force Windows to Rediscover Monitors
Whenever Windows sees a new monitor it adds it to the end of the current configuration. However, this doesn't change the current configuration.To force Windows to configure monitors properly if the numbers aren't correct, you need to delete these two registry keys, and then add the monitors one at a time.
Alternatively, copy the text below into a text file and call it Monitor Persistence.reg, save it, then run it to remove these entries:
Windows Registry Editor Version 5.00