Don't forget that all your old console utilities work just fine in PowerShell:

PS> hostname
KEITH1

Long form:

get-content env:computername

Short form:

gc env:computername

All above questions are correct but if you want the hostname and domain name try this:

 [System.Net.DNS]::GetHostByName('').HostName

A slight tweak on @CPU-100's answer, for the local FQDN:

[System.Net.DNS]::GetHostByName($Null).HostName

In PowerShell Core v6 (works on macOS, Linux and Windows):

[Environment]::MachineName

hostname also works just fine in Powershell

An analogue of the bat file code in Powershell

Cmd

wmic path Win32_ComputerSystem get Name

Powershell

Get-WMIObject Win32_ComputerSystem | Select-Object -ExpandProperty name

and ...

hostname.exe

The most descriptive way for me is:

[System.Net.DNS]::GetHostByName($env:COMPUTERNAME).HostName

You can store the value as follows $name = $(hostname)

I want to add that simply executing $name = hostname will also save the localhost name of the PC into a variable.

Not specifically for Powershell version 1.0 and more of an overview of different possible ways to get information via Powershell:

• Native CmdLet (usually the best, but sadly really slow to get the Computername):
  (Get-ComputerInfo).CsDNSHostName
  Returns the "Name of local computer according to the domain name server" (Info about Get-ComputerInfo, Info about its return value)
• Classical CommandLine executable:
  hostname.exe
  Returns the "host name portion of the full computer name of the computer" (Info about hostname.exe
• Environment Variable:
  $env:COMPUTERNAME
• Registry:
  (Get-ItemProperty HKLM:\SYSTEM\CurrentControlSet\Control\ComputerName\ActiveComputerName).ComputerName
• Static .Net Property:
  [Environment]::MachineName
  Returns "the NetBIOS name of this local computer." (Info about the System.Environment class)
• Property of COM-Object (Computername via deprecated Scripting-Api):
  (New-Object -ComObject WScript.Network).ComputerName
  Returns "the name of the computer system." (Info about the WshNetwork Object, Info about the Windows Script Host Objects)
• Property of WMI-Object:
  (Get-CimInstance -ClassName Win32_ComputerSystem).Name
  (Info about Win32_ComputerSystem)