To resolve the issue please do the following:
- open License Portal and delete the Core from Cores list. It's safe to do so
- on the Core machine, open regedit and navigate to HKEY_LOCAL_MACHINE\SOFTWARE\AppRecovery\Core\CoreSettings\DisplayName
- change DisplayName to the actual machine name or just delete the value completely
- stop and start the Core service
Core will contact License Portal and register its new new properly.