There are multiple ways on how we can find citrix xendesktop database server name:

1. via powershell: Use command Get-ConfigDBConnection (or Get-BrokerDBConnection) on the delivery controller. Both these commands will show your database server, instance name and database name.
2. Using registry: Navigate to “HKEY_LOCAL_MACHINE\SOFTWARE\Citrix\XDservices\ ConfigLoggingSiteSchema\DataStore\Connections” registry key on the delivery controller and check value of key, ConnectionString. This will have same information as above powershell command. This will be useful if server is not responding to any powershell commands.
3. In your Citrix studio, click on Configuration. You will see Site database, monitoring database and configuration database there.