Just fire the task without async/await.

private void InitMethod(ServiceControl serviceControl)
{
    if (serviceControl != null)
    {
        Task.Factory.StartNew(() => serviceControl.Execute());
    }
}

In a proper F&F task all exception handling (including a final catch, logging, notifications) is done by the task itself, so you don't need exception handling that async/await provides.

Make the method name reflect what it does. I wouldn't mind a name like FireAndForgetXyz

Just fire the task without async/await.

private void InitMethod(ServiceControl serviceControl)
{
    if (serviceControl != null)
    {
        Task.Factory.StartNew(() => serviceControl.Execute());
    }
}

In a proper F&F task all exception handling (including a final catch, logging, notifications) is done by the task itself, so you don't need exception handling that async/await provides.

Make the method name reflect what it does. I wouldn't mind a name like FireAndForgetXyz