In the US, it's the other way around per the FDA. The common name should be the primary name. Include the INCI name as the secondary, if you wish to include it.
"...common names are required, and when used as a secondary listing, Latin names are accepted. Although the “INCI name” (which usually means the Latin name) is commonly thought to be required, it isn’t – it’s optional....
"...For botanicals, the name should be either as identified in the CTFA Cosmetic Ingredient Dictionary, Second Ed (1977) – which listed botanicals by their common English name – or if not listed there, the name generally recognized by consumers. Either way, the correct wording is the common name, which complies with the FPLA [Fair Packaging and Labeling Act] requirements...."
Source:
http://blog.mariegale.com/botanical-names-ingredient-declarations/
Additional information from FDA:
https://www.youtube.com/watch?v=akPq1tsbze0