I've moved your post to our ePO area for better attention by an expert.
Are you saying the agent is uninstalled from the client when the client is renamed? If so that is not default behavior but the ePO server can be configured in such a way to make that happen. For example if you have a AD Sync group defined such that "When systems are deleted from the synchronization point:" the action is set to "Delete the systems from the System Tree" and the check box is selected to "Remove the agent from the deleted systems" that could explain this behavior. When configured that way when the AD Sync task runs it would look at the AD groups its syncing and if client machines exist in the ePO system tree that do not exist in the sycronization group those machines would be deleted from ePO and flagged for agent uninstall. Then next time the agent communicated in it would uninstall itself. This behavior is by design and if it is problematic for you then you should remove the check next to "Remove the agent from the deleted systems" in the AD Sync group configuration page.