The Name and the ProcessName properties of the Get-Process, Stop-Process and Wait-Process CmdLets seems to use the wrong process names compared to the Win32_Process WMI class and other process related tools such as Windows task manager.
Where WMI and task manager lists task names like Notepad.exe or Calculator.exe, Get-Process returns just "Notepad" or "Calculator" and Stop-Process requires me to specify these shortened names too.
I understand that I can get the full name of the executable by specifying the -FileVersionInfo with Get-Process but it still doesn't allow me to search for a process using it's real process name.

Couldn't at least one of the Name/ProcessName output properties list the full name of the process and couldn't the ProcessName input parameter accept both variants?
If not, can you at least add input/output properties that works with the full process name?