I have done some searching for your specific setting. It appears your contact forms are customizations as their is no fild for " Second Name". In options > Contacts, the default filing order can be set with use of the full name or Last,first / Company / last, first / company last, first.

Is your contact form a customization?
You stated you can manually file them using second name, does that option for second name show in the options?

Keep me posted?