Create event log entry with powershell and fill in user
Even though (as far as I'm aware) Write-EventLog does not provide an option to write directly to the "User" field, you have two workarounds:
Use built-in standalone exec "EventCreate.exe" (type in eventcreate /? to see the manual)
This one does support providing the username field. I'm not sure, but it may require a password for that user too.
Second workaround would be to pass $env:USERNAME to the "message" field of Write-EventLog. This way you will still obtain the environment's current user.
I hope that helped.