my understanding of the labeling requirements in the US is that soap that is intended for washing is not required to be labeled at all. soap that is intended for a cosmetic or medicinal purpose DOES require labeling.
that being said, even though no label is required, it is permitted. if we choose to label, we need to follow specific guidelines. ingredients must be listed from highest to lowest quantity, and must be worded using the scientific name of each ingredient. we can list what goes into the pot, or what comes out of the pot (oils and lye OR saponified oil of whatever), but not a combination thereof. many people choose to list what comes out of the pot in order to avoid using the words lye or sodium hydroxide, but either way is correct.
First, labeling is required per the Federal Trade Commission's Fair Packaging and Labeling Act. So a label is required for soap in the U.S.
Edit to clarify:
Ingredients may be left out for soap that is only soap and not a cosmetic or drug, BUT the other labeling requirements must be met.
Second, Intent is not the only factor which determines the labeling requirements of soap. There are other factors, such as how the soap is perceived by the public or the customer. There are common perceptions about certain ingredients that make some soaps cosmetic, or drugs, or both, no matter what the soap maker intends. AND if the customer does in fact say they are buying a particular soap for cosmetic or medicinal reasons, that will mean the soap should be labeled as such.
BUT for just plain soap without those types of ingredients, the common name and not the scientific name on the ingredients list is still acceptable within the US regulations at this point.
This is a quote from the FTC regulations directly from the US government website:
(3) require that the label on each package of a consumer commodity (other than one which is a food within the meaning of section 321(f) of title 21) bear (A) the common or usual name of such consumer commodity, if any, and (B) in case such consumer commodity consists of two or more ingredients, the common or usual name of each such ingredient listed in order of decreasing predominance, but nothing in this paragraph shall be deemed to require that any trade secret be divulged; or
The URL for the page upon which that is found:
http://uscode.house.gov/view.xhtml?req=granuleid:USC-prelim-title15-chapter39&edition=prelim
FTC Fair Packaging & Labeling Act:
https://www.ftc.gov/enforcement/statutes/fair-packaging-and-labeling-act
Incidentally, if you check your state regulations, you may find the exact same wording in your state regulations as well. It's in many many state regulations in the US. So even if the Feds drop that requirement, you still have to follow the laws in the states in which you sell soaps.
More about Common Names by Marie Gale, the foremost expert in the US on labeling requirements for soaps and cosmetics made by folks such as ourselves:
https://www.mariegale.com/what-is-the-common-name/
That could change in the future, of course. There are bills before Congress addressing some of these things. One change will be that they are now being called Personal Care Products.
Additionally, there are hazardous ingredients labeling regulations as well, and in some cases, the potential exists wherein soap might be required to include such labeling. (Example: soap with toxic substances included as an ingredient. - I have seen people discuss adding turpentine to soap, for example.)
https://www.cpsc.gov/Business--Manufacturing/Business-Education/Business-Guidance/FHSA-Requirements/