Expanding on René Nyffenegger's answer, for those who do not have access to PowerShell version 6.x, we use Split Path, which doesn't test for file existence:
Split-Path "C:\Folder\SubFolder\myfile.txt" -Leaf
This returns "myfile.txt". If we know that the file name doesn't have periods in it, we can split the string and take the first part:
(Split-Path "C:\Folder\SubFolder\myfile.txt" -Leaf).Split('.') | Select -First 1
or
(Split-Path "C:\Folder\SubFolder\myfile.txt" -Leaf).Split('.')[0]
This returns "myfile".
If the file name might include periods, to be safe, we could use the following:
$FileName = Split-Path "C:\Folder\SubFolder\myfile.txt.config.txt" -Leaf
$Extension = $FileName.Split('.') | Select -Last 1
$FileNameWoExt = $FileName.Substring(0, $FileName.Length - $Extension.Length - 1)
This returns "myfile.txt.config".
Here I prefer to use Substring() instead of Replace() because the extension preceded by a period could also be part of the name, as in my example. By using Substring we return the filename without the extension as requested.