Let's start with the original artificial sweetener, saccharine. It's chemical name is benzoic sulfimide and its chemical formula is C7H5NO3S. It's quite simple in structure with a benzene ring fused to a five membered ring sulfonamide. It is commonly known in the US as Sweet N' Low. But the taste of saccharine wasn't the best so other sweetners were sought.
Another popular sweetener is aspartame. Its structure and name are more complicated. The chemical name is N-(L-aspartyl)-L-phenylalanine methyl ester and its chemical formula is C14H18N2O5. Structurally, it is basically two amino acids attached together, aspartic acid and phenylalanine. It is commonly known in the US as NutraSweet.
Finally, a more recent artificial sweetener is sucralose. It is commonly known in the US as Splenda. Unlike the other two sweeteners, sucralose actually is a sugar but the human body is unable to digest it so it passes through the digestive system and provides no calories. It is chemically almost the same as the natural disaccharide sugar sucrose (table sugar), except that three hydroxyl groups have been replaced with chlorines. Its chemical formula is C12H19Cl3O8.