I've had the same problem, and think I finally fixed it. I've rebooted 3 times without the "please uninstall" popping up". The trick seems to be based on the fact that DDM 1.x was made for them by a third party named EnTech, and their registry keys still exist after the uninstall.
We recently upgraded our fleet of a mix of Latitude, OptiPlex and Precision to Dell Display Manager 2.0 and recently up to 2.1.0.45. So many users are complaining that it keeps asking to uninstall the older version of DDM. "please uninstall your older version of dell display manager" An older version of DDM is nowhere to be found on the system.  When you click the box in the dialog to uninstall, you are taken to Programs and Features that only lists the current version.  It's just the same loop upon every single reboot, or when you connect your device to another display. Both the 2.0 and 2.1.0.45 version of ddmsetup.exe were downloaded directly from the support website.  Uninstalling 2.0 or 2.1.0.45 does not help.  When you install either 2.0 or 2.1.0.45, the same message returns asking to uninstall. Can anyone advise on how we can continue to use this tool in peace without getting this prompt to uninstall something that doesn't exist?
Uninstall Older version of Dell Display Manager