Select-String is probably not the hammer you wanna use for this particular nail (see below) :-)

Get-Process has a -Name parameter that takes a wildcard:

Get-Process -Name nginx
# or
Get-Process -Name *nginx*

To kill the process, either call Kill() directly on the object:

$nginxProcess = Get-Process nginx |Select -First 1
$nginxProcess.Kill()

... or simply pipe the process instances to Stop-Process:

Get-Process -Name nginx |Stop-Process

As you can see, we never actually need to locate or pass the process id - the Process object already has that information embedded in it, and the *-Process cmdlets are designed to work in concert - PowerShell is all about command composition, and this is an example of it.

That being said, Stop-Process is also perfectly capable of killing processes by name alone:

Stop-Process -Name nginx

How did I know the *-Process cmdlets had a -Name parameter?

Apart from reading the help files and documentation (I get it, I don't want to read anything either unless I absolutely have to ;-)), a quick way to learn about the parameters exposed by a cmdlet is by running Get-Command <commandName> -Syntax:

PS ~> Get-Command Stop-Process -Syntax

Stop-Process [-Id] <int[]> [-PassThru] [-Force] [-WhatIf] [-Confirm] [<CommonParameters>]

Stop-Process -Name <string[]> [-PassThru] [-Force] [-WhatIf] [-Confirm] [<CommonParameters>]

Stop-Process [-InputObject] <Process[]> [-PassThru] [-Force] [-WhatIf] [-Confirm] [<CommonParameters>]

The output shows us 3 distinct "parameter sets" (combinations of parameter input accepted by the command), and the required and optional arguments we can pass to it.

What's wrong with Select-String?

The Select-String cmdlet is the PowerShell cognate to grep - it takes some input, and performs regular expression matching against it based on whatever pattern you give it.

But grep is only useful when you're operating on strings - and as you've already found, Get-Process returns structured .NET objects, not flat strings.

Instead, the PowerShell-idiomatic approach is to filter the data, using the Where-Object cmdlet:

Get-Process | Where-Object Name -like '*nginx*'

Here, we instruct Where-Object to only let through object that have a Name property, the value of which must satisfy the wildcard pattern *nginx*.

Where-Object also supports arbitrary filter expressions, by accepting a scriptblock - PowerShell will assign the current pipeline object being evaluated to $_ (and $PSItem):

Get-Process | Where-Object { $_.Name -like '*nginx*' }

... which you can extend to whatever degree you need:

# Only let them through if a specific user is executing
Get-Process | Where-Object { $_.Name -like '*nginx*' -and $env:USERNAME -ne 'Quarkly'}

In powershell you would do:

gwmi -query "select * from win32_process where name='PROCESSNAME.exe'" | %{if($_.GetOwner().User -eq 'USERNAME'){$_.terminate()}}

One of the nice things about PowerShell, is you usually don't need to store values. You can just pipe commands together.

Something like this should work:

Get-Process | Where-Object { $_.Name -eq "myprocess" } | Select-Object -First 1 | Stop-Process

And the breakdown is:

1. Get-Process gets a list of all of the running processes
2. Where-Object filters the list of processes to only those whose "Name" is equal to "myprocess"
3. Select-Object the -First 1 selects the first entry from the list
4. Stop-Process stops the process passed to it

Using the $PID built-in variable which returns the current process ID, this will kill off all others.

Get-Process -Name powershell | foreach {
    if ($_.Id -ne $PID) { Stop-Process $_ }
}

This script should be run from the console or remotely, but not from the ISE since that has a different process name. Alternatively you could do this:

Get-Process -Name powershell | where { $_.Id -ne $PID } | Stop-Process