$pdt = Get-BrokerPrivateDesktop DOMAIN\MACHINENAME
Get-BrokerUser -PrivateDesktopUid $pdt.Uid | Add-BrokerUser -PrivateDesktop “DOMAIN\NewMachineName”
My Contribution / Reference / Spare Time
$pdt = Get-BrokerPrivateDesktop DOMAIN\MACHINENAME
Get-BrokerUser -PrivateDesktopUid $pdt.Uid | Add-BrokerUser -PrivateDesktop “DOMAIN\NewMachineName”