I recently had a situation where I was trying to determine where the VMM database was in my environment. It would not start because the database was not online. The registration on the VMM server provides this information under: HKLM\SOFTWARE\Microsoft\Microsoft System Center Virtual Machine Manager Server\Settings\SQL in the MachineFQDN and/or MachineName field shown below.
Summary: Looking for a quick way to find out what server hosts your VMM database? Log into the VMM server, open regedit and look for the HKLM\SOFTWARE\Microsoft\Microsoft System Center Virtual Machine Manager Server\Settings\SQL\MachineFQDN or HKLM\SOFTWARE\Microsoft\Microsoft System Center Virtual Machine Manager Server\Settings\SQL\MachineName value.