ETA: Okay, that' s actually a bad example for the oils... sorry I should have looked at it closer. The blog post mentioned you can elect to label as either what goes into the pot (water, common oils and sodium hydroxide) or what comes out (just saponified oils). FDA now wants what goes into the pot listed.
That example shows the INCI names of the oils. According to most recent FDA guidelines, you must use common names of oils. As an option, you use INCI names of oils. If you decide to also include INCI names, you must do so for all the oils on your label.