Firstly, it's important to know that the FDA has not defined the term “natural” or "vegan" and has not established a regulatory definition for this term in cosmetic labeling. FDA also does not have regulations for the term "organic" in cosmetics. The U.S. Department of Agriculture (USDA) regulates the term for agricultural products. Always read labels and ingredient lists.
Learn more on FDA labeling regulations here: https://www.fda.gov/cosmetics/resourcesforyou/industry/ucm388736.htm#3