Usually when you remotely connect to a Server Desktop either via RDP or Citrix, the default Domain should be your domain, sometimes the server name appears instead. To change the server to display the domain as default you can either log onto the server’s console (or mstsc /console or mstsc/admin) with your domain account, then log off or you can make the following registry change on the server
HKLM\Software\Microsoft\Windows NT\CurrentVersion\Winlogon\DefaultDomainName