For Plex server to use your old data, you will have to move them from
C:\Users\my name\AppData\Local\Plex Media Server
to
C:\Users\my name-DESKTOP\AppData\Local\Plex Media Server
(while Plex server is not running!)
Or you could use the opportunity and move the Plex data folder to a more convenient location, or even a totally different hard drive.
So that the next re-installation goes less problematic. [HowTo] An extended guide on how to move the Plex data folder on Windows
