Sorry for the late answer, I just saw your post this morning.
SuRun Stores User Settings in the Windows registry with the scheme "HKLM\Security\SuRun\<ComputerName|DomainName>\<UserName>".
That's why the settings are gone after renaming Computer but not SuRun's Registry keys.
[Edit:]
I changed SuRun's behavior in 1.2.1.3b3:
http://forum.kay-bruns.de/post/4070