The quick story is that we comply with Health Canada/INSI regulations which stipulate that the ingredient has to describe what happens after we process it into a product.
Thus here's a quick guide to the original ingredient when you see a name (more to come):
Sodium Cocoate started as Coconut Oil
Sodium Olivate started as Olive Oil
Sodium Avocadate started as Avocado Oil
Sodium Apricot Kernelate as Apricot Oil
Sodium Cocoa Butterate started as Cocoa Butter
Sodium Sheabutterate started as Shea Butter
Sodium Ricinoleate started as Castor Oil
And yes, Aqua is Water!
The longer story:
It's because we follow the requirements of Health Canada and INCI. INCI refers to the International Nomenclature for Cosmetics Ingredients. It is a system for naming ingredients used in cosmetics that is multilingual, multinational, and based on Latin. The use of INCI names is mandatory in Canada for all manufacturers and retailers of cosmetics, whether artisanal or industrial. The complexity of this jargon can be intimidating for consumers (and sometimes even for manufacturers!). However, the INCI is designed so that ingredient names can be universally recognized, thus avoiding the potential confusion that would arise from the use of various—even improvised or inadequate—trade names.
Health Canada also stipulates that we can't list ingredients as they are when they go into our mixing bowl or pot (like Olive Oil and Coconut Oil). Instead we have to list the final ingredients in products after our "manufacturing process" like soapmaking. This means that instead of Olive Oil, we have to list the saponified version of the oil, Sodium Olivate in this case.