How do I get the localhost name in PowerShell?

You can just use the .NET Framework method:

[System.Net.Dns]::GetHostName()

also

$env:COMPUTERNAME

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

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)
• Static .Net Method:
  [System.Net.Dns]::GetHostEntry("").HostName
  Returns the DNS Hostname (fqdn) of the system (Info about the System.Net.Dns.GetHostEntry Method)
• 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)
• P/Invoke a native API function:

Add-Type -TypeDefinition @'
    public enum COMPUTER_NAME_FORMAT{
        ComputerNameNetBIOS,
        ComputerNameDnsHostname,
        ComputerNameDnsDomain,
        ComputerNameDnsFullyQualified,
        ComputerNamePhysicalNetBIOS,
        ComputerNamePhysicalDnsHostname,
        ComputerNamePhysicalDnsDomain,
        ComputerNamePhysicalDnsFullyQualified,
        ComputerNameMax,
    }
    public static class Kernel32{
        [System.Runtime.InteropServices.DllImport("Kernel32.dll", SetLastError = true, CharSet = System.Runtime.InteropServices.CharSet.Auto)]
        public static extern bool GetComputerNameEx(COMPUTER_NAME_FORMAT NameType, System.Text.StringBuilder lpBuffer, ref uint lpnSize);
    }
'@
$len = 0
[Kernel32]::GetComputerNameEx([COMPUTER_NAME_FORMAT]::ComputerNameDnsFullyQualified, $null, [ref]$len); #get required size
$sb = [System.Text.StringBuilder]::new([int]$len) #create StringBuilder with required capacity (ensure int constructor is used, otherwise powershell chooses string constructor for uint value...)
$len = $sb.Capacity #get actual capacity of StringBuilder (important, as maybe StringBuilder was constructed differently than expected)
[Kernel32]::GetComputerNameEx([COMPUTER_NAME_FORMAT]::ComputerNameDnsFullyQualified, $sb, [ref]$len);
$sb.ToString()

Returns "The fully qualified DNS name that uniquely identifies the local computer. This name is a combination of the DNS host name and the DNS domain name, using the form HostName.DomainName. If the local computer is a node in a cluster, lpBuffer receives the fully qualified DNS name of the cluster virtual server."
(Info about the GetComputerNameEx API function, Info about the COMPUTER_NAME_FORMAT enumeration, used c# signature of COMPUTER_NAME_FORMAT (unofficial), used c# signature of GetComputerNameEx (unofficial), short blogpost about P/Invoke in powershell)
Note: Use P/Invoke with caution. Sufficiently incorrect usage can actually make powershell crash. The Add-Type call is somewhat slow (but only needs to be called once in the script).