This will write out the SQL aliases on the local machine in a human readable form

Get-SQLAliases.ps1

$aliasRegistryPath = 'HKLM:\SOFTWARE\Microsoft\MSSQLServer\Client\ConnectTo'
(Get-Item $aliasRegistryPath).Property | ForEach-Object {
    $aliasName = $_
    $aliasTarget = Get-ItemPropertyValue $aliasRegistryPath -Name $aliasName
    
    $aliasTargetType = switch ($aliasTarget.split(',')[0])
    {
        'DBNMPNTW' {'a named pipe'}
        'DBMSSOCN' {'a tcp port'}
        Default { ("an unknown target: '{0}'" -f $aliasTarget.split(',')[0]) }
    }

    $aliasTargetServer = $aliasTarget.split(',')[1]
    $aliasTargetPort = $aliasTarget.split(',')[2]

    if ($aliasTargetPort)
    {
        Write-Host "Alias: '$aliasName' points to '$aliasTargetServer' using $aliasTargetType via port '$aliasTargetPort'"
    }
    else
    {
        Write-Host "Alias: '$aliasName' points to '$aliasTargetServer' using $aliasTargetType"
    }
}