In your scenario, since you don't have administrator privileges to create custom event log sources and names, you are constrained by what the system already has available for logging. The Write-EventLog cmdlet requires a source to be registered before it can write to a log, and trying to use a source that doesn't exist or isn’t registered will throw the error you encountered.

Unfortunately, without administrative rights, you cannot register new event sources using New-EventLog. However, you can still write to the existing logs if you identify the logs and sources that are already available to the user.