The ingredient name you use ultimately comes down to where you are selling your product. Assuming US, then the proper name to use is what is listed in the INCI dictionary as published by the PCPC.
From the FDA rules…
Identification of Ingredients by Name
The name established by the commissioner as specified in § 701.30.
The name adopted for the ingredient as listed in:
(a) CTFA Cosmetic Ingredient Dictionary
(b) United States Pharmacopeia
(c) National Formulary
(d) Food Chemical Codex
(e) USAN and the USP Dictionary of Drug Names
The name generally recognized by consumers
The chemical or technical name or description
This is the order of priority. So, if there is a name established by the FDA, that is the one to use. After that, if there is a name used by the INCI Dictionary (the old CTFA Cosmetic Ingredient Dictionary), then you use that. If there is no established name, then go to US Pharmacopeia…etc. But if the name appears in the INCI dictionary, that is what you are required to use.