In PowerShell it is relatively trivial to retrieve the domain for the logged in user, as this is stored in the environment variable. In multi-domain environments it is often the case that the user account is a member of the same domain as the computer account. To retrieve the domain name of the current computer the following command can be executed:

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[System.Net.NetworkInformation.IPGlobalProperties]::GetIPGlobalProperties()

To only retrieve the Domain Name the following command can be used:

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[System.Net.NetworkInformation.IPGlobalProperties]::GetIPGlobalProperties().DomainName

For more information about the GetIPGlobalProperties method and the IPGlobalProperties class please refer to the following article:
MSDN – IPGlobalProperties