During the software installation, three installation specific security groups are created in the domain where the member server hosting a ChangeAuditor coordinator resides:
ChangeAuditor Administrators - <InstallationName>
ChangeAuditor Operators - <InstallationName>
ChangeAuditor Web Shared Overview Users - <InstallationName>
These group names may not meet AD naming policies in place,etc.
Moving the groups should be fine as long as you don't alter the SID of the group or change permissions in such a way as to prevent the coordinator from reading the group's membership & contents.
Renaming of the Change Auditor AD groups is not recommended, but if the AD group SID matches the one listed in the AzManXmlStore.xml file you should be fine.
Please view KB 139692 for further details